Alas Comma

Yes, because it's parenthetical.

Interjections are always hard to intercalate. I think you have these options:

But alas! Her heart...
But—alas!—her heart...
But alas—her heart...
But alas, her heart...

That's iffy. You have started the sentence with a coordinating conjunction that when used in its usual place encompasses the comma for appearance' sake. "I wooed her, but alas, her heart belonged to another." We drop the first parenthetical comma and let the one before "but" suffice because there's just too many commas otherwise, and this sort of structure happens a lot. Even so, I would put one i

Going by the rules, I would put a comma before "alas." However, as others have pointed out, this construction is "iffy" for a variety of reasons. When in doubt with commas, use the sound quality of the sentence to determine its use. Do you want a short pause before "alas" or would you prefer "but alas" to read as one unit without pause?