Will average household incomes rise if Republican tax cuts become law? Not for long. Average cuts will be small and they won't last. In the House version, the middle fifth of the households may see their after-tax income rise by 1.5% in 2018, but most of that increase will be gone by 2027. The richest 1% of households get a larger increase--2.5%--and they still be getting most of it in 2027. 
But won't tax cuts for the rich and the corporations generate many more jobs and higher pay? Probably not. There is no evidence that tax burdens on businesses and investors are the reason that job growth is not faster or that wages are never on the up-escalator for very long.
The purchasing power of an hour's work for average employees increased 53% from 1950 through 1975. But wages took a U-turn in the 70s and they fell or stagnated in the 1980s. The latter occurred despite the fact that rich people were gifted with much more after-tax income in the Reagan era. Between 1980 and 1982 the top marginal tax rate was cut from 70% to 50%; from 1986 to 1988, it fell to 28%, the lowest level since 1931. The corporate tax rate was also slashed. Despite these incentives, average hourly pay fell 4% (1980-1990). 
Dropping individual tax rates for rich people does not lift average Americans. Neither does cutting corporate taxes, as long as there is a plentiful supply of jobless workers and few strong unions. Don't expect a big jump in real business investment when many companies already have more money than they know what to do with. How much more stuff can they sell if household incomes don't increase substantially? 
But I am engaging in a fact-based discussion of economic policy and social justice. That's not what Republican promises are all about. The new tax cuts may add a little economic boost as government revenues don't grow as fast as spending--it's Keynesian deficit spending, and Republicans do it all the time--but it's unlikely that there will be sustained wage increases. Higher pay for workers has never been a Republican goal, and nor is it for quite a few Democrats. Republicans are in charge and if they really cared about workers, they could raise the federal minimum wage to $15 and start infrastructure programs today. They might actually help unemployed left-behinds in Ohio, West Virginia, Detroit, and Chicago. And they'd win Democratic support on both issues. But most Republicans aren't interested in good-job policies or cooperation across the aisle. Many, especially members of the Tea-Party/Freedom Caucus, have a gimme world-view that elevates the capitalist ethic of greed into a moral code. They're for YOYO (You're On Your Own), not WITT (We're In This Together).
If a right-wing House Republican leader were talking privately to his colleagues in an honest and realistic way, he might sound like this:
"Just among ourselves--doing things to create more jobs and more income for the lower half--that's not important. Talking about it is good, but I haven't thought much about it. We are doing the tax cuts to reward corporations and our big donors; we need their money--that's politics. But we also have idealistic motives--our own moral theory. Affluent and rich Americans deserve everything they can get their hands on, regardless of how they do it and how many jobs they kill. They work hard amassing wealth. Sometimes they create a lot of jobs; sometimes they get rich by destroying jobs. Often they make money by employing lawyers and lobbyists to evade taxes and rig legislation. Hey, that's life; more power to them. It's good that their kids start out way ahead of John and Jane Doe's kids, and the kids will have more of a head start when we get rid of the Estate Tax. And why not? These are obviously people of good stock.
"Think of it this way. We are cutting government to boost Social Darwinism. That's the struggle that lifts everyone"well, everyone who has what it takes. The federal government is 90% burden. We know it never creates jobs. Market competition is what makes America great. American was greater in the 1800s when the Robber Barons and their servants could tell the truth about defective workers and did not have to be dainty about crushing worker rebellions. We need more of that. Selfishness is good. You should all read Ayn Rand's Atlas Shrugged. It was published in the 1950s but it is still relevant. However, it's longer than our tax bill. If you are too busy for Atlas, here's a short variation that comes with God's approval. In many public lectures he gave in the late 1800s, a man named Russell Conwell said this: a poor man is one 'whom God has punished for his sins... remember that there is not a poor person in the United States who was not been made poor by his own shortcomings or the shortcomings of someone else. It is all wrong to be poor anyhow.' Invigorating, right? We need more of that today. Here's a motto for us: Selfishness good. My money going to help average Americans bad." By the way, this statement may not be appropriate for all audiences.
 On the House bill, Tax Policy Center, "Preliminary Distributional Analysis of the Tax Cuts and Jobs Act," November 8, 2017, especially Figure 1. On the Senate proposal, check the graphic in David Leonhardt, "The G.O.P. Is Fooling Itself on Taxes," New York Times, SundayReview, November 19, 2017, 3.
 Wage information based on The Economic Report of the President, 2016, Table B-15.
 Josh Bivens, "Real World Data Continue to Show No Link Between Corporate Cuts and Wage Increases," from Economic Policy Institute, November 3, 2017, found at https://portside.org, November 12, 2017; and Eduardo Porter, "Tax Cuts, Sold as Fuel for Growth, Widen Gap Between Rich and Poor," New York Times, October 3, 2017, accessed November 15, 2017, at nytimes.com.