I can not assist you in avoiding the authorities, but i will provide certain basic information to you. State DMV's do share information, especially in this computer day and age. However, if your warrant is not related to a DMV matter in Alaska, I doubt that the Colorado DMV would have that information. Of course, it is still possible that they would have "most wanted" information. So, the more serious the matter, the more likely it is that they would have the information. Further, DMV officials are not the police, and can not arrest you on a warrant. All they could do is notify the police that someone with an outstanding foreign state warrant came in to the DMV office. Then, the police could follow up with you based upon the information you gave the DMV.
The best solution is not to ignore, but to deal with the foreign warrant head on. Usually, it is not as difficult or as bad as you think. It is always worse to wait until they find you. Please speak with a criminal attorney in Alaska to discuss how you can resolve the warrant and the underlying charge. Remember you are innocent until proven guilty, and outstanding warrants on less serious matters lose steam over time. The longer you stay away and out of trouble the less likely they are to care about the outcome. Witnesses become less available, memories fade, and they will be less likely to want to spend the money to pay for the cost to extradite you to Alaska.
I hope this answers your question, and good luck in resolving your legal issue.
The short answer to your question is yes your warrant will show up in Colorado. The issue in your case is what type of warrant you have. If they are seeking some type of felony extradition back to Alaska or if it’s some type of misdemeanor failure to pay. Also I have to ask were you ordered to pay by the state (plea deal) or did you take it upon yourself to pay back the money on your own. If you are just trying to pay money back to the aggrieved party I would suggest getting an extradition lawyer in Alaska.