That makes sense.

The mountain/ fountain rhyme occurs earlier than The Rose, in Tannahill's Braes of Balquihither, published 1812, where it's a 'siller fountan'. But then how many rhymes are there for mountain? No particular reason to think there's any borrowing here.

But there probably is in Francis McPeake's reworking, Wild Mountain Thyme, where is a 'crystal fountain'. Inevitably he'd have been familiar with the Rose of Tralee from childhood, like everyone else in Ireland.

I hasten to say I'm not in any way criticising the honourable tradition of borrowing and echoing earlier songs.