But ASR-based tools in theory would allow such an operation mode, but I have not seen aligners that read from the mic buffer directly or have a built-in option/CLI for it.
Knowing the text in advance basically means that you can train your own language (textual) model adapted to that exact text, and then use the (standard) acoustic model for your language and aligning procedure as usual. Hence, I am quite sure you can tweak e.g. CMU Sphinx or Kaldi to do it. Perhaps gentle (which is based on Kaldi) is worth looking into.
You need to deal with imperfect matching because the ASR might produce a text slightly different from the ground truth, but if you want to chunk e.g. at sentence granularity (and then move on to the next sentence), you should be able to do it in real time.