Sbrum25, welcome to the forum!
If you've read many of Bill Cody's perch postings here, you undoubtedly realize getting YP to thrive in a pond with LMB is difficult. That said, you certainly could add some perch large enough to avoid being snacks for the bass. They'd better be 5" or more; even some of these will be attacked. Some will make it. It is likely that you will have to restock every couple of years as recruitment may be rather low with LMB and BG predation on the fry.
I'll share are some of my experiences. 8 years ago we bought our place with 1/4th-acre pond that had been in existence for 20 years. We were told there were LMB, BG, BCP, YP in it. All we caught or saw were LMB, YP, and two large GC. There were no sunfish at all. There were no weeds nor any other cover. The first several years I added brushpiles and let submergent weeds become established.
Three years ago I added BG; two years ago I added GSF. These sunfish were hopefully to take some of the predatory pressure off the YP, our preferred panfish. I've hammered the bass population to the point that we don't see bass every time we walk the pond or fish it. I've added YP twice.
We now have practically 100% of the muddy bottom covered with vegetation-Elodea, some short clumpy grass-like plant I have not identified, a very few duck potatoes, a few American pond weeds, and FA in summer. The perch are doing better with all that cover. The BG struggle as the water temps are on the cool side. The GSF achieve fair recruitment. I cannot say that anything is thriving. I hand feed Optimal Blue Gill. We have a few RNBT and tiger trout and 7 GC presently.
All of this is to say that with heavy harvest of the bass, I've been able to get some other fish to recruit young. I don't get many large panfish; we catch a couple 9 and 10 inch GSF and BG each season. They're original stockers. YP grow only to 10". Nearly all LMB are under 11 inches; unfortunately, there are either 2 or 3 greater than 20" bass that have been uncatchable for 3 years. These biggest bass are a major problem as they can eat anything. I hook them each year, always on very light line; they dive into the cover and break off. I've invited others to fish the pond in hopes that their different fishing style will prompt the big ones to bite. Shotgunning is prolly the answer. Or draining the pond. Ha ha.
I'd say buy or catch some perch and throw them in. They cannot hurt. You'll end up with a few or several. I can't imagine their upsetting your BG/LMB population.
I'm no expert; others will chime in, maybe even the big perch doctor himself.
Once again, welcome to Pond Boss. Enjoy!
