No, I wouldn't - several times I've added oils or conditioners to my henna, and I feel like it poorly affects my hair's absorption of the dye. That said, I have naturally oily hair and tend to mix my henna with undiluted lemon juice as an astringent treatment for my scalp and roots, and the lemon juice helps the henna brighten my already-dark hennaed hair as well as give a good stain to my virgin hair. Maybe it would work differently for you, but I haven't had the best of luck with it, and I hate washing out henna after hours and hours, only to see that I wasted 100g of powder (and have super gross henna-scented hair without the beautiful red gleam! ugh)
I shampoo henna out with a 50/50 mixture of shampoo and conditioner, then condition again to get all the rest out, and rinse for about 15 minutes. My hair's always a little dry afterwards, so oil treatments are good. I dip my ends in hot olive oil if they're extra unruly.
