Will the legs be able to take the load? Absolutely. Will the entertainment center top itself need to be pretty sturdy due to not having a ton of support? Yeah. Is this fairly normal for things with legs? Also yes. To me the only thing that really different about this is the fact that you're using three legs instead of two. This is of course assuming a wood top. A glass top would probably need more support in the center.

Wood species and joinery would be critical. A through tenon and an oak might be enough. Middle would likely be a bit "soft" , support would be coming from the three ends.

I think it would be okay, but you would want to make sure the joints are glued nicely.

Depends.

What sort of joinery are you using? What sort of would are you using? How much weight are you putting on top of them?

Personally, I'd add some sort of extra reinforcement. With all the valuable, delicate, and expensive electronics on top, I wouldn't risk it. You could do some tests first and see how you feel about it, though.