Can I still come down on recruiting orders even if I have less than 18 months left in my AD contract?

All enlisted assignments, in all branches of the military, work like this -
You are placed on assignment.
The assignment incurs an SRR.
You reenlist to meet the SRR or you sign a Declination and get out.
You can still be placed on an assignment with a shorter SRR like Korea if you have enough time left on your contract.

Technically yes. Branck/HRC gives you the option to either accept the orders and re-enlist/extend to cover the assignment, or decline the assignment. That normally leads to a bar on re-enlisting. Normally Branch try's to look at DEROS/ETS dates before selection.

Technically it’s possible.

In the Marine Corps it’s certainly possible. The screening team looks for eligible candidates for special duty assignments and flags them as eligible. I have seen Marines get flagged for recruiting and those recruiting orders are waiting for them if they ever return to active duty. But I’m not sure how that function is managed in the Army