まし is usually used to mean "preferable" in the "less bad" sense, i.e. you're choosing the lesser of two evils. ぐらいなら reinforces this point, i.e.
魚を食べるぐらいなら飢えたほうがましだ If I had to go as far as eating fish, starving would be less bad.
ぐらい can come after nouns as well, but with this specific nuance, it is not often used after nouns. So we could say
恥をかくぐらいなら死んだほうがましだ Dying is preferable to facing disgrace
However, if we're using the noun 恥, it would be more natural to rephrase to よりも (or よりは)
恥よりも死のほうがましだ Death is preferable to disgrace
By the way, your example sentence is comparing a noun to a verb, 恥 and 死ぬ. While maybe not exactly wrong, I feel rewriting 死ぬ to the noun 死 sounds better.
Beware that ぐらい can also be used in the opposite sense, to reinforce that something is easy or small (like "only"). In this sense, it's used after nouns as well
ちょっと待つぐらいならいい I don't mind waiting (if it's only) for a bit
ケーキ五個ぐらいなら食べられる If it's only 5 cakes, I can eat them