can you add apple care to an existing watch and then send in for repair?

Your post hints that you wish to add AppleCare+ for an Apple Watch which already needs repair. This will not be possible, because Apple would wish to test or examine your watch to prove it is in good condition before accepting it for AppleCare+.

There is a second constraint. In most regions AppleCare+ cover must be added within 30 days after purchase. Your profile suggests you have an Apple Watch Series 6, which will be much older than this limit so it would not qualify.