A judge most certainly can impose probation to include community service, restitution etc. without a conviction. It can be done with an agreement from the Prosecuting Attorney's office for Deferred Prosecution for one, in that case they agree to defer the prosecution of the case for a set period and the offender agrees to certain terms. If he successfully completes those terms then prosecution is dropped. It goes no further. No conviction.
A second possibility is what is referred to commonly as an SIS, Suspended Imposition of Sentence. In this case the offender does enter a plea of guilt, the Court does NOT impose a sentence, there is NO conviction. This is often done in non-violent cases such as child support. Probation with terms follows and the offender can complete probation with, technically, no conviction. This one can be a bit tricky because there was a plea entered, just no conviction. It can count as a conviction for sex offender registries and some firearms laws. Depends upon the jurisdiction.
The equivalent of deferred prosecution in some states is to have a conviction, do probation, and then go back to court where the Judge expunges the case. In this instance there is a conviction during the period of probation, and not after, assuming successful completion of the term of probation.
I am sure there are a few more possibilities, but these are the basic ones any others would follow.
Considering what your friend is on probation for the PO is absolutely correct in assuring and insisting he has no access to weapons. In my opinion the PO is not correct in attempting to control who else has those weapons.
In your friend's case there is for sure a written out agreement signed by all parties to include the judge. Your friend for sure has a copy of that agreement. You may want to take a look at it if he permits it.