Lack of light should not cause any issue. You could use the semi-opaque bisquine plastic, that would allow in light but still keep out drafts if you feel like you want more natural light. Just make sure it's heavy stuff, not the thin flimsy stuff they sell as paint drop cloths.
Good for you in finding those drafts! I have drafts in my living areas that I still haven't tracked down. The snake room is more secure than the rest of my house!