No.
Ryan Air is a ULCC. Southwest is a LCC. They are very different.

The European market is basically comprised of the big national legacy airlines (BA, Air France, Lufthansa) and the ULCCs (Ryan, Easy, Wizz). There really isn't an equivalent of Southwest in Europe, especially anywhere near its scale. Sure, the big national legacy airlines have tried to create their own LCC spinoffs but they are not like Southwest.

My point being, the ability for the ULCCs to achieve the same market share in the US as they have in Europe is hampered by the existence of Southwest here.