This depends based on where you are, but in most places, absolutely, yes.

English ivy is horridly invasive in most places it lands in.

Invasive is regional, of course, so check online with local botanical resources. But unless youre in its native range, its probably invasive.

It tends to only flower when it climbs, and birds eating the berries is the genuine worst way for it to spread, so a lot of places keep it as ground cover because it grows so damn well. But it always escapes eventually.