i believe quite a few wireless mice do this to conserve on battery.
my old logitech mx1000 used to do the same thing.
you get into a habit of "micro-moving" the mouse every few seconds if you are stationary in a fps game. a very very slight movment (like a hand tremble) will keep the mouse awake. no it will not affect sniping or other gameplay factors.
ultimately i couldnt say it adversely affected gameplay. while undesireable the freedom of no mouse cord was worth it. the r/f wireless mouse didnt lag because of it being wireless either. i'm not sure about bluetooth mice.