Not all companies on the slope use union labor. It depends on the company – some are exclusively union, others are not. A third group will hire a mix of union & nonunion workers depending upon their contract with the client.
If a client requires organized labor then that's what they'll get. If it's not a requirement then it's up to the contractor to decide.
I recently had the opportunity to work for a heavy civil construction company that hires primarily union workers. Since my job was to provide required safety training, I spent time with every new employee plus the folks coming back from R&R. I grilled them about the ins & outs of union work on the slope and they were happy to share what they knew.
Here's what I found out:
If you're a laborer and you are in the office when a call comes through, many times you'll get the job ahead of folks who might be higher up on the list than you are. It pays to be in the right place at the right time.
You can call companies direct and ask about openings. Some businesses accept resumes and will request specific people, but you must be registered with the appropriate chapter office.
Be nice to the office staff & use good phone manners. If you're rude, demanding or generally unpleasant then you won't get called up.
Be sure you show up with the appropriate personal gear: Cold weather clothing, gloves, boots with safety toes (check with the company about specific requirements), etc. Brooks Range Supply in Deadhorse has a decent selection of products but there's no guarantee they'll have what you need in your size.
Don't forget to bring your NSTC card to the slope! You can't get a badge without it.