If you get Drill orders before marriage, are you and your duel military spouse doomed to be separated?

Congrats on the upcoming nuptials!

Short answer: Yes, you're stuck until he PCSes. However, he can request a compassionate curtailment of his orders (not likely, but the answer is always 'No' if you never ask).

Make sure the two of you are enrolled in the Married Army Couples Program (MACP)* This will ensure that joint domicile assignments are considered for the two of you as you go forward. It's not a guarantee, but the program does have a high success rate of placing married couple's assignment in the vicinity of each other.

A couple of tips in your situation.
1) Have you explored Space-A travel? If there are flights into airfields nearby it might be the answer to your $1k tickets.
2) The MACP isn't a silver bullet - it's more of an aspirin for the headaches you'll have juggling dual military careers. You'll both face some tough choices at times - do you take a so-so job so they can have a career enhancing one? Do you both endure separation so you both can have a bite at the apple? etc.
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* MACP - https://www.hrc.army.mil/content/Married%20Army%20Couples%20Program

Getting married and enrolling in MACP doesn't cause your spouse to move, it just causes your branches to attempt to put you two together at your next move. Military spouses are not usually stationed together for Drill or Recruiting. Drill is only two years, so there's no way his branch is going to move him to your location, even if there was a place for him because when it's time for you to move he would have less then 24 months on station. The goal for most locations is 36 months, anything less requires a waiver. Anything under 24 requires an even higher level waiver. Even if you guys could start everything now, there's no chance he could PCS within the next six months.

He could ask for a Permissive Reassignment under MACP, although it's unlikely that the strengths support his MOS and Skill level at a Tradoc installation. A Permissive Reassignment is where a person shoulders all the PCS cost and is not eligible for any reimbursement whatsoever. Even the travel has to be while he's on leave. Moving from Alaska, unless his life fits in the back of a truck, that's an expensive option - if it's approved because he's still obligated to be there till his DEROS.

The most common outcome to this is that you two enroll in MACP and when it's time to move they place him somewhere that can support you both when you complete your tour. He can even request a curtailment, although since he wouldn't be PCSing to your location, it probably wouldn't be supported.

Until you both are married and both enrolled into the MACP, the dice will have to be rolled to see if they will PCS to your location. Your soon-to-be spouse could try contacting their Branch Manager and request your base...but those are not good odds. A Compassionate Reassignment request wouldn't even be considered. But, even if married and enrolled in MACP, there is no 100% that you both would be assigned to the same base come PCS time.