When to answer and when not to answer a brief e-mail from a busy academic?
My own busy-person email triage has three tiers:


No response needed = near-zero cost
Minimal response needed = minimal cost
Response with significant thought and care needed = significant context-switching cost


A brief "thank you" email would go into category #1: no bother or burden, but noticed and appreciated all the same.  In other words, send the email: it's not a significant nuisance, and it's nice to be appreciated.