What happens if you Install Yes Man on the 'big screen' in the Lucky 38, but you do the rest of the quests for Caesar?

Yes Man's face is on the big black screen in the Lucky 38 but you're doing quests for Caesar, i.e., absolutely nothing - it isn't so far down the independant quest line that it stops you from proceeding with the others.

Nothing really happens, you can still complete all of the Legion quests without failing Beware the Wrath of Caesar.

If you mean what happens after the end of the game, then I would say that Caesar would probably have you (the Courier) disable Yes Man permanently, as well as disable any Securitrons on the network.

I upgraded the securitrons but im currenlty doing the Legion quests, was that a clever thing to do or doesnt it affect the Battle of Hoover Dam?

doesnt effect the battle since yes man takes orders from you but cant do anything gameplay wise and yes man/independant was designed as the failsafe questline aswell incase the player messes up House, NCR and legion questlines/reputations

ahh so incase i mess up with the legion, i can always fall back on Yes man

Yes, the independent quest line (Yes Man) is the one that you can always fall back on even if you mess up every other option.

Isn't it also the canon ending? But RP wise I think it would be a good idea to install Yes Man while doing Caesar's bidding. Since Yes Man takes orders from you, the Legion would have no problem taking over Vegas since the security of the strip will be under your control. Though I would imagine Caesar would order you to stop using the machines since he doesn't think too highly of technology.