No, it just mean "sound" as in "stuck".
sŵn = "sound, noise" in general e.g. Clywais i sŵn rhyfedd (I heard a strange sound), Beth ydy'r sŵn 'na? (What's that sound/noise?)
sain = "sound, audio" in a more technical sense e.g. Technegydd sain yw e (He's a sound/audio technician, effaith sain (sound effect), ton sain (sound wave), sain gytseiniol (consonant sound) etc.
English is my native language, and I've never used the word "Sound" to mean "Stuck".
You would win your bet. When I say that though, the 'sound' bit means 'in good health' Nothing to do with 'stuck'