No. Before "that", only "it seems" works. "there seems" is not always wrong though.
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AnonymousThere emerged that truth that Jacks had been convicted of burglary before.This is possible, but the grammatical structure is different. It parses as "(There emerged) (that truth that Jacks...)", not "(There emerged that) (truth that Jacks...)".
AnonymousThere emerged the truth that Jacks had been convicted of burglary before.Yes, still OK. In fact, "the" is more probable than "that" in this sentence.
Are they still correct?
(There emerged) (the truth that Jacks had been convicted of burglary before.)