2010 stglide If I plug a hand held cb unit into the cig. Lighter and use the cb while riding will it compromise any electrical component or over heat the cig plug?

Shouldn't be a problem. Cigarette lighter should be wired and fused for 20 amps, although not intended for continuous use. What's the amperage of the CB. Should be a lot less.

I would just double check the amp on CB unit and that of the lighter. Also, I have known many people, who have a dedicated lighter plug wired just for this, ruing though separate breaker to the battery, so it does not go though the breakers with the other electronics.