A repeater won't necessarily increase performance. It will definitely increase range, and one would *hope* the improved signal reliability would increase performance to some degree. But all repeaters have a significant downside -- they cut your effective bandwidth IN HALF!
The repeater and primary router are typically using the same frequency, which means the repeater can only be actively communicating w/ either the primary router or a wireless client at any given time. IOW, one or the other is always waiting for the other to complete its transmission can begin. And that results in a loss of bandwidth that's approx. HALF of what you'd normally expect. Add another repeater and it's halved again.
So I guess the answer is, maybe a repeater will improve performance, maybe not. Just depends on whether your current range is so poor (and by extension resulting performance so poor), that a repeater would still be an improvement, despite the loss of bandwidth. This is why I tell ppl that repeaters are really about improving range. Any performance improvement is questionable, and to the extent it exists, incidental.