Different light fixture in basement on pull switch
The short answer is yes you can, the easiest way is first to see if all the lights are on 1 breaker (normal wiring) It is possible they could be on 2 or 3 different circuits but again you could still do it with 1 switch (3 phase and some wires). 
Most basements or all I have worked on are fed from 1 or 2 circuits. Identifying the circuits is the first step. After that it can be as simple as turning all the pull chain fixtures on and interrupting the feed with a simple switch a box on the feed or even at  the panel , 2 wires (Romex to a new box) where you install a simple switch). This may be quite easy but we need to know if it is a single circuit and if it is for lighting only.