They can probably move you with very few problems. My shared hosting server was shifted over to Portland recently.
The new Portland datacenter is likely much less expensive to operate than downtown LA. Additionally you get new hardware, they don’t actually physically move your server, they set up the new one with a copy of your files and then switch from old to new with a DNS change.
While my account is on shared hosting and not a dedicated server, dreamhost has moved my account to a new server probably about every 12-18 months since I’ve been a customer. Only one of these has ever had any kind of glitch, and support had that fixed about 30-40 minutes after I let them know the problem.
I wouldn’t worry too much, it shouldn’t cause too many headaches.