So i got this quest after doing lots of stuff for the NCR (which i'm going to side with). Now what will happen if i continue this questline? Obviously i'll have to do alot of stuff which will most likely hurt the NCR. Should i exit Caesar's tent and do other quests, or is it safe to continue anyway? I haven't got a similar quest from NCR, so that's why i'm asking.

Depends on how you handle the mission, you can either keep the bots for yourself or destroy them like Caesar asks.

Yeah, but if i do this questline, will it hurt my relationship with NCR in any way? Or is this questline part of the main story (and it supposed to be completed)?

Its part of the quest line. And no it wont hurt NCR rep unless you help Caesar of course