Short answer, yes....straight from the buns to the garden.
It's fine straight on the garden, fresh bun berries, urine and all. No composting is needed with rabbit manure before adding it to the garden (unlike chicken or goat or other animal waste that will burn). I've planted directly into nothing but pure fresh rabbit waste in bags or bins (no added soil) that's given good drainage with more than excellent results.
Some folks like to spread it out and dry it up for a day or so but that's not needed at all. Unlike other animal waste, rabbit waste including urine, is pure cold-gold to gardens. The waste I sell I will sometimes spread out to dry a bit at times depending on what the customer (erroneously) believes.

I charge more for that because it envolves extra time & labor.
The big bin trays I have under my buns (simple square drywall bins) are drilled with many holes to let a lot of the moisture drain out naturally into a wicking subfloor....but not that that's needed at all for use in gardens...it just makes for a bit more sanitary area between cleanings and gives the tubs a little lighter weight for me (or my helpers) to haul out ever couple of weeks when removing from the barn to the garden or drying area.
Goat manure comes a close second to rabbit manure, but goat manure MUST be composted before use, unlike rabbit manure. If you're wanting to feed the
plants (instead of the
soil) and don't want to use the pure rabbit manure for whatever reason (I can't imagine why), rabbit manure tea (using the liquid from a few pounds of manure in a sack steeped for a couple of days in a 5 gallon bucket of water) is also literally pure garden gold for topical feeding. When possible, feeding
the soil with the raw manure is best instead of feeding the plants only...and rabbit manure straight from the barn feeds the soil and plants without risk of burning plants, UNlike fresh goat/chicken/other manures are capable of doing.
