Slugs never did anything to improve the holdover with my air rifles. If anything, the trajectory was less flat than with lighter pellets.
I went through a brief but unproductive period of using them with my 25 Career 707 rifle. Even at close to 100fpe it couldn't really stabilize them past 40 yards (give or take). It was fun taking out squirrels at close range with them but hardly worth the super high cost.
There was nothing I could kill with a 55gr slug that I couldn't kill better with a 43gr pellet (as I could actually hit something with the Eun Jins)
The few air rifles that shoot slugs well are made specifically for the purpose in terms of barrel choice and energy. I don't know what twist rate they all use but they are typically at least twice as powerful as similar caliber pellet guns. The ones that do well at long range (like 200 yards) are the extreme big bores which put out 300-1600fpe.
I have never tried 22 slugs but the ones you have are fairly light so maybe you'll have better results than I did. I've tried slugs up to 58gr in my 25 Cricket. They work but not with usable long range accuracy. There was no damage or anything like that.
The main thing in deciding if you can try slugs is what they are made from. If they are 100% soft lead and of the appropriate diameter then you should be able to test them in the Mutant.