Absolutely! You have too much riding on that rubber to fudge a few bucks on a balance. Not balancing will give you flat spots and unusual wear. A good balance will be both for spin and side-to-side balancing. It will also tell you if your tire/rim is beyond balancing (defective).
Along with balance, tire pressure and regular inspections are extremely important. For instance, I was checking our 16' tandem axle cargo trailer before taking a long road trip. Noticing something unusual on the hidden side of one tire, I found that the tread was separating. Had it not been replaced, it would have failed in the first hundred miles.
Trailer tires take a heck of a beating, from tandems scrubbing and torquing on a turn, to weight shift and sway, to catching road debris, to just being poor quality. In the past 10 years of towing 4,500+ mi/yr, we have replaced 6 tires by necessity-four times on the road. In all instances, they were balanced brand name tires. We have come to carry 2 spares.