No, but Audacity does have a “snapping” behaviour when you are lined up with audio clip boundaries or labels.
I made a plug-in for creating labels at “beats per minute”. The idea of this is that you can then quickly and easily create a label track that lines up exactly with a click track, and you can then line things up more easily with the click track. See this post: Beat Per Minute labels
Instructions for installing Nyquist plug-ins here: https://manual.audacityteam.org/man/installing_effect_generator_and_analyzer_plug_ins_on_windows.html#nyquist_install