Word for people who ask to be treated but never accept when offered

Solution 1:

I'll take the liberty of slightly altering your sentence:

"Just invite him. He'll not join us anyway, he is [a bit] X"

X being:

• reserved (Probably Likes - Possibly won't come)
• withdrawn (May Like - Won't Come)
• reclusive (May not like - Certainly won't come)
• noncommittal (Likes - Won't Say Whether or not will attend)
• uncompanionable (May not like - Won't come)
• solitary (Likes - May not come)

all those would fit into your example sentence to convey that the person may not come to the event, but not all of the persons will like being asked, because some like no interaction (not even the asking).

Solution 2:

I thought of two closely-related words that have almost opposite meanings: (1) "ingratiate" - trying to get into someone's favour, but having also the sense of insincerity, and (2) "ingrate" - someone who is ungrateful for the favour or kindness shown. Perhaps the person you are trying to describe is an "ingratiating ingrate"!!