Strava does download maps as one rides, depending on the screen one is on.

I think much of what it does is when one completes the segment (at home by WIFI?). Every time it seems to download maps and recent segments by oneself, and one's followers. Uploading a completed segment always seems to be unbelievably slow.

It might be interesting to do an experiment of traveling with Strava enabled, and having it off, and looking at the data use logs. I agree, probably not that significant, a few megs, at least if one starts/stops while connected to WIFI, and perhaps keeps it off the mapping screens.