I'm not sure if it means "very long time" in this sentence. If it means that, what does the 「っ」 do in the sentence?
ジョーのやろうは刑{けい}務{む}所{しょ}へたたっこまれるようなことになるんでしょうか?
It's the passive of たたっこむ, which is an elided form of 叩き込む, which here figuratively means 'to throw someone in prison'. Thus a translation might be:
That bastard Joe, could it be that he's going to end up getting thrown in prison?