In most cases, yes, though it depends on what tickets you received.
Most traffic offenses can be paid online. However, DUI type offenses (statute number 61-8-XXX), Driving While Suspended/Revoked, offenses with jail possible, and Careless Driving where the driver is under 25 years of age require personal appearance.
Additionally, by state law any "Title 45 offense" i.e a charge with a statute number 45-X-XXX requires a person to personally appear, and then to be fingerprinted following their initial appearance.
For most other offenses, you may pay online at: http://citepayusa.com
You will need to select "Montana" then "pay a citation" then "Missoula County Justice Court."
You always have the option to see a judge to discuss your case or to enter a not guilty plea. Online payments are merely a convenience for those who do not wish to dispute the charges against them.