Can I rally with no pit crew members on my team?

Yes, you can. It won't be as easy, naturally, but it's still doable. Most rallies these days have all their service areas in one location on each day. So, in practical terms, you would get up earlier in the morning, drive the rally car and the truck you towed to the rally with that has all your tools (your 'service rig') over to the service area. Park it there, and drive the rally car back to the start area.

This becomes a little more difficult if you're a single biker with no crew, or if there are multiple service areas in that day. For that, we go to time honored Plan B: get one of the other rally teams to drive your service rig around, or just ask around to throw a bag of tools and a jug of gas into someone else's service rig.