Again, no. Any institutional investors who can't take part in a private Tesla have an effectively limitless amount of shares that they need to get rid of. They have the choice:
A) $420, during the buyout; or
B) Greater than $420, selling to shorts
So obviously, they want (B). The problem is that their supply vastly outpaces the number of shorts that needs to cover. Now, if they could all coordinate their actions, they could say, "Okay, none of us sell until the stock hits $600, then we'll each sell X% of our holdings". Except that they can't do that. That'd be illegal. So it's a free, open market, where supply outstrips demand.
If party A tries to sell at $600, party B is going to look at that and think, "I don't want to be stuck with all my stock sold at $420; I'm selling at $599." To which party A will look at that and think, "Well, I don't want to be stuck with all of my stock at $420; I'm selling at $598". And so on and so on. It's a race that will resolve itself virtually instantly; indeed, it'll never get to $600, or anywhere close, because everybody knows how this is going to play out. Their stock will sell only marginally over the $420 price point because they have more to get rid of than shorts need to buy, and nobody wants to get stuck with only getting $420 for all of their stock.
If it wasn't for investors that have to liquidate, I'd agree that it could go well over $420. But because they exist, and because they surely well outnumber shorts that need to cover, I can't envision this massively-over-$420 short squeeze that some here are envisioning.