How big of an area?
Not knowing that, if you arent planting til May-June I think that would be fine if that matl. was mixed into a regular mulch or compost application & even worked into the surface a little. What is the likelihood of wet weather between now & then? If its dry to drought wet the area a couple times a month.
Hope that helps.

Thanks for the reply.
I live in southern Oregon. Hard to predict the level of precipitation between now and June. It should be mostly wet. I'm concerned the nutrients from the rabbit manure might wash out before June.

My raised bed is 6' x 20'. I grow primarily hot/exotic peppers, i.e., scorpion, scotch bonnet, habanero, bhut jolokia, 7-pots, ajis...

With sufficient organic matter in put your soil will be fine for the plants you mention. If I'm not mistaken southern Ore. zone 8 has a lot of clay so you want a lot of organic matter in your soil. Yes there will be nutrient loss but not so much as to be a detriment to your garden. Regular applications of compost will ensure healthy, well drained soil & nutrients readily available when plants need them.

The Plant Hardiness Zone (8 in this instance) has nothing to do with the soil type one has. The only thing the PHZ tells us is which plants will survive a normal winter in that area.
What you, roguejim, plan to do is not mulching but is tilling, Working any material into the top 4 inches of soil is not mulching.
Whether the nutrients in that rabbit manure might leach from the soil depends on how much organic matter you have in the soil to help capture those nutrients. Adequate levels, about 6 to 8 percent OM, will be enough to hold most nutrients in place.
Levels of organic matter less than 2 percent have been shown to not hold nutrients very well at all.
Far better for those nutrients would be to compost that manure instead of simply adding it to your soil, unless a good reliable soil test indicated it was needed in the soil.

Peppers are well known to tolerate any amount of fertilization, you should be OK. If there is enough bedding, a lot of the nutrients will not wash off.

Thank you everyone for the helpful responses. Is there a soil test that will determine the % of organic matter in my soil?

Perhaps these simple soil tests might be of some help.
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.