Yes, Google insists on keeping your offline map fairly up to date. (I consider that a good thing, after driving for years on out-of-date Garmin maps.) Don't bother downloading a map for Europe now if you aren't going for three months. You can do it right before you leave or even after you get to Europe if you'll have WiFi. Just put it on your "to-do" list.
The offline map takes space on your device. Yes, it is a detailed street map. But the larger of an area that you download (Google lets you choose the size), the more space it will take. If you have a phone with limited storage space, remember that the map takes space away from photos, videos, etc. that you might want to save on the phone. If your phone has the ability to add a memory card to add more storage, consider doing it - these memory cards have gotten quite cheap. I just bought a 128GB microSDXC card for my Android phone for $35 on Amazon.
I suggest you try out Google Maps "offline" at home if you are curious about how it will work. Download the "offline" map for where you live, then put the phone in airplane mode and ask the phone for directions somewhere. It's a little different than the "normal" Google Maps navigation...but it works. Delete your "home" area map after your experiment so you'll have enough space to download the offline map for your destination.