Can an upstream fault trip a downstream GFCI?

Have a GFCI outlet that trips every time it rains hard, always resets right away and rarely trips again with the same rain storm. On that breaker are two upstairs bathrooms and a garage (3 outlets total, w/ 1 GFCI in bath), all inside under roof. Plugged into that circuit is a freezer (GFCI tripped before that was added), a FIOS ONT unit powered via UPS unit and an window unit air conditioner (already eliminated as cause).