Can I use a regular road jersey for cyclocross racing?

You can, but you'll likely encounter two major issues: rear pockets catching on the top tube during shouldering (which can cause you to stumble or drop the bike), and the jersey absorbing mud and water instead of shedding it. For your first few CX races, a road jersey is fine, but if you continue racing, a CX-specific jersey will meaningfully improve your experience and safety.