As you can with (for example) Cross DJ. I have done it, but it’s not like you are controlling your decks like you would with a controller, unless you bring an extra controller/pad to use FX, slices and stuff. Essentially using HID mode with CDJs turns your DJ software into track management software pretty much. The buttons on the CDJ are all you can use and they do exactly what it says on them.
So while it may sound like a good plan and it’s ok to do if you just want to show up with your laptop and DJ “traditionally”, but I wouldn’t support the notion that it’s the best way to DJ.
Best bet would be to get a controller WITH built-in sound card (which is the majority these days), but I understand the money/time short bit.