Kind of, yes. The people voted democratically to elect Joe Biden as President in November. The Constitution and laws say that he becomes President Elect on Jan 6. That's the law. People vote -> President elect on Jan 6, President on Jan 20.
What happened on Jan 6 was that the transition of power was, for a number of hours, prevented through violent means. Thank God two things happened on Jan 6: (1) Mike Pence refused to leave the Capitol and (2) Mitch McConnell refused to entertain the 10 objections that they wanted (which would have delayed proceedings for at least 20 hours). If either of those two things happened, we'd be in a political situation uncovered by the Constitution and law. That's when things get bad, because either side is just making things up at that point. It becomes a battle of wills and political power; whoever has the most power to reify their will, wins.
The plan on Jan 6 was to delay certification as long as possible, because there was a pressure campaign ongoing in which states were being pressured to "decertify" their votes, and Pence was being pressured to consider alternate slates of electors for Trump.
I think everyone needs to start getting clear on the facts here:
(1) Jan 6 was about stopping Biden from being certified as President Elect by any means, because that's a write only operation. There's no undoing that. Once he is certified by the House, Senate, and VP, the deal is done. Not even the Supreme Court can overturn that: separation of powers and all.
(2) The legal way to do that was spelled out in the Eastman Memo [1]: It argued Pence could just unilaterally refuse to consider slates of electors and cause a contested election, which favored the Republicans electorally. But Pence would not go along with this plan.
(3) Pence was aware of fraudulent certificates of the vote that had been submitted by various states, which purported to be legitimate votes for Trump. Pence could not go along with accepting those without a pretextual reason given by the states themselves. This was the last piece of the plan which was, supposedly according to Trump's lawyer, coming together at the last minute while the Capitol attack was ongoing.
Think of it this way: On Jan 6 the situation was that every state had certified their votes, Trump lost 62/63 court cases and the Supreme Court refused to hear the case, the AG had said he found no fraud. There was no pretext for Pence to accept the alternative electors.
However, that could have changed very quickly had the pressure campaign continued. If Pence had left the Capitol on Jan 6, then the joint session would not have reconvened for several days while the Capitol was secured (actually the Capitol was correctly deemed insecure by Secret Service the day of Jan 6, so there's as open question as to why Pence was there in the first place). At this time, there was a pressure campaign going on to get one or more states to "Decertify" their certificate of the vote. Had one or more states done so, it would be very easy to see how this would have ended up at a contested election where Republicans would have all the votes needed to install Trump as President.
[1] https://en.wikipedia.org/wiki/Eastman_memos