Assisted GPS just uses mobile data via the cell to download the initial catalogue of where the satellites are. It just helps get a fix quicker but is not required. You could be standing around for quite a while to get a fix though. In fact I find that often when riding anyway even in the UK as I have no phone signal often where I ride so it takes ages to lock on.
Assisted GPS will basically be turned off if your data is off. Some phones have an option to disable assisted GPS entirely, or to enable/disable it when roaming so might want to check that. It’s a small amount of data but abroad it can still work out expensive.
Strava app if using that will just do the tracking but won’t be able to upload or download data. Then see if you can find wifi at some point and upload with that.
p.s. in Europe, check out bundled data from your operator, though watch out. EU rules mean by default you get capped on your data but means you run out and can’t use it any more. Operators try to push their bundles instead but these automatically opt you out so you are back to unlimited and can run up big bills. Check the bundle deals to see if they’re any good. Some do a daily amount so you can use a fair amount per day for a couple of quid. Others give you a fixed amount per month. Often rubbish, like 30mb (considering smart phones can eat through half a gig in a month!). When you go over your bundle it reverts to prices that are £s per Mb.