The short answer is yes and no.... This applies to moderate middle most as the extreme positions will not be swayed either way.
Before a good answer can be given, it depends on what you call success. Another 8-8, 7-9 season is not success in my mind - although that may be this teams ceiling through no fault of Alex. So let's define success. For me success is 10+ wins. With that in mind (yes = it will matter, no = it will not matter):
You di not ask this part, but it needs to be addressed, anything less than 9 wins is a negative on the FO. But I think you will see most blaming the FO not Alex. At least that's where I will be. Alex is who he is. Most of us knew what was coming. A more conservative version of Kirk. Less mistakes but also less heroics. But it's not his fault the FO brought him here and may be expecting something different. He is who he is by now. And that's a decent QB who will not typically lose games for you but will also not often win games either.
Dan - No, even a SB will not change my mind that he is a POS. I can however separate the football side and will obviously have to give him credit for finally after 20 years putting a winning combination together. But just a little. Even a blind dog finds a bone sometimes.
Bruce - Yes, sort of. Not happy with how he handled Kirk and his spend thrift approach to Free Agents is too focused on money and not enough on player quality as he is just not a good evaluate of players. When someone like that has the final say you end making poor personnel decisions - like having your oft injured starting LG be a guy that sat in Free Agency long enough you could sign him for basically league minimum. But hey, if it produces a winner, I will have to give him credit. Having said that, nothing will change many peoples mind on how Bruce coughed up a fur ball dealing with Kirk. It's not just about keeping Kirk or not, Once they decided to move on they did so the only way possible that they got zero compensation for a legitimate starting NFL QB in his prime.
FO Structure - No - This is the real issue most of us have here. If there was a true GM with a real football personnel evaluation background then many would feel better about the chances of this working. The question for Dan is, there are many examples that show the best recipe for success in the NFL and his method has shown almost no results, why keep doing it?? So if they have success, you have to give them some credit. But it's also fair that after almost 20 yrs to have the feeling that they more got lucky than found a true structure for success. Having said that, if it's the start of a string of successful seasons then that mindset may change. But not after a single season.
Alex vs. Kirk - Yes - Have to give them credit for getting Alex if it works out. It's more than luck. They clearly targeted the best QB in free agency not named Kirk Cousins and landed him. For many of us, the trade in a vacuum is not a problem - outside of not getting anything for Kirk. Alex is a capable QB. You get a safer but not quite as dynamic QB. For me, I do not think it's a big drop off between the two. Kirk does sling a bit more at the end but that often ends in a painful interception. I believe Alex shows a bit more confidence than Kirk, especially on broken plays. But it's only two games and has yielded only one win in those two games. There is a lot of football left.
In the end, the answer to your question is probably winning cures everything, at least to some extent. So maybe for some it will vindicate the FO or change people minds more than others.
However, what you are seeing being relatively new to the board, last weeks loss is just so representative of the Redskins of the last 20 yrs, many of us are just really tired of seeing the same movie over and over again. A rebound win over the Packers could revive some hope. Let's hope they have a great game. Two weeks of agonizing over a 1-2 start after a great first game would be painful. Although, to be honest, a loss would give me reason to do something else on Sundays and just look for a score. Something I started last year after close to 50 yrs of watching almost every minute of every game live.