There will be a little effect from that, and one-of-each could happen, but I think that the average person is incorrectly reasoning about this in the opposite direction. I've seen a lot of people thinking basically, "Each candidate has about a 50% chance of winning, so the chance that the Democrats win both is 50%*50% = 25%." The results of both elections will be extremely highly correlated, though, so that line of thinking is totally wrong, and it's giving a whole lot of people the wrong intuition.
I have no idea who's going to win. If the Democrats win, it will be the Republicans' own fault in many different ways. I don't worry about it too much, since their control of both the Senate and the House will be too narrow to do anything too shocking, though I do think that it'd be much better for the Republicans to maintain control and for us to get 2+ years of total gridlock.
I have to say, the sheer idiocy of so many Republicans has been making me root for the Democrats a bit, even though from an ideological/utilitarian perspective I think gridlock is better than Republican control which is better than Democrat control. Any person or institution that is this incompetent, irrational, and unwilling to even privately believe uncomfortable truths deserves to fail utterly and be replaced by people who actually have working brains. (There's plenty of irrationality and living in bubbles on the Democratic side as well, and in humanity as a whole, but it's really gotten insane in the Republican party.)
Turning to the electoral vote counting tomorrow: Probably it will be basically like normal but with 2 hours of pointless and predictable extra speeches from both sides, with many Republicans basically just putting on a show to be able to say "hey, I tried." But I was thinking today about how it could possibly go off the rails:
First, there will be a large number of pro-Trump armed protesters there. I suppose I could imagine them storming the capital, overwhelming the fairly weak police forces in and around D.C., and Trump intentionally not using his resources to stop them, so that they are able to actually disrupt the vote count. This could last for a few days, maybe, before the government apparatus including the military work together to arrest Trump for treason or whatever. Trump would eventually totally fail, but it would be a huge shock to the American psyche.
Second, it seems to me that the law allows Republicans to filibuster the counting process. They could just endlessly submit objections, and if Pence goes along with it, then each objection results in 2 hours of debate. They could extend it all the way to Jan 20 if they want. Now, this would be extremely stupid, since there is no end-game. The whole process would grind on and on, with almost everyone across the country and in Congress growing to despise this process and Trump. Kind of like the impeachment, but in the opposite direction and much worse. It'd be a good thing to do if Republicans want to try getting Trump's approval down to 5%. And then on Jan 20, Pelosi would by law become President, so what have you gained? Maybe a competent President with tons of support among both the bureaucracy and the people could use the uncertainty surrounding this whole unprecedented succession issue to successfully stay in power, but Trump is nowhere near being able to pull that off. However, several Republicans seem to be thinking about nothing except what their base supporters will say on Twitter over the next 6 hours rather than doing any sort of sane planning, and if enough of them are like that, this mess could maybe occur. (I do think that Pence has to go along with it, though.)
But if enough Republicans are sane, they will try to get this over with as soon as possible, sticking their necks out as little as possible. Nobody should've committed themselves to signing onto these objections in the first place (just politically, not even thinking about ideology), but that ship has probably sailed.
(Note that the winners of the Georgia race will not be certified in time for it to have any impact here unless maybe if things do go way off the rails.)