No.
OBS' Audio subsystem will compensate up to 1 second, but there is no back and forth with that and the VST plugin (i.e. once you get the delay up to that amount OBS will continue to compensate by the highest amount and not back down, even if the source of the delay is gone). That said everything will stay in sync in general.
I mention all of this because there are some plug-ins that have a delay of over 1 second (UAD AKG-BX20 I'm looking at you), and those tend to cause issues. If you have such (or a chain that goes over 1 second) then you should simplify your FX chain, or use a DAW to process your audio and port that to OBS.