I've done this a lot - mostly with big machinery where the ANC on the earbuds, or the (not aviation quality) ear muffs alone don't suffice to bring the noise down to an acceptable level.
It works well - but have them in long enough, particularly when physically working and the earbuds will loosen and shift. The seal on the earbuds with your ear canal is important, especially with ANC buds. Removing face shields and ear muffs to re-adjust earbuds is frustrating.
Interesting. I've used earbuds inside earmuffs quite a few times and not had this problem, except when the cord gets tugged.
I definitely agree with the principle that if the experiment is fast and cheap, just do it.