Pumping while pregnant

So Iv never tried to pump colostrum while pregnant but want to try this time when the time is right. Iv seen people try to at 34 weeks and up. Just curious, if I were to start pumping, does only the colostrum come in? Or can your milk potentially come in too and then you have to pump while also trying to deliver baby? I produced quite a bit with my first born & my milk came in at like day 2 so I’m just concerned I’m gonna produce while being pregnant. Has this happened to anyone? Or maybe that’s not even a thing I have no idea.