An MVR wouldn't show accident claims, it will only show your past tickets or citations. If an insurer paid out for a claim, the most likely report they're using is called a CLUE report.
Coverage & Claims
Typically, if the police are not involved, the accident will not show up on your motor vehicle report (MVR). However, the accident may show up as an at-fault accident on the CLUE report which is the report that pulls and verifies prior insurance claims.
To dispute your Motor Vehicle Report (MVR) you will need to contact the Department of Motor Vehicles. The MVR comes from Colorado's state records of violations.
Car Insurance Costs
Based on the fact that you received a ticket for the accident, the accident will be listed on your motor vehicle report (MVR) regardless if you file a claim or not. Having the accident on MVR means that your insurance rates will be impacted even if you pay out of pocket for the accident.
It depends how it is marked on his MVR. If it is still an open case and no conviction has been issued you can answer no because during the reporting process it will not show.
Most driving records insurance companies run will show the claim paid under "no fault" or "not-at-fault" and should not affect your rates at all. If your current car insurance quote reflects the accident as "at-fault," present the evidence you have in your favor and get a new quote.
While it can vary by car insurance company, most insurance companies will charge (rate your premium) for any ticket or violation for 3 years. However, after that 3 years you won't be charged.
It may still be listed on your CLUE report if the accident was reported to insurance, but there is a chance that the accident may not yet be listed on your report. It's also possible that there could have been a clerical error and it never got listed.