Perhaps this paper from UC Davis will be helpful. You will note that oats can be seeded into Bermuda grass ... so maybe mulch would not be a problem. But maybe putting a layer of soil on top of mulch will aid sprouting ... roots will find their way through mulch to reach soil. anyway, hope you find this helpful.

COVER CROP DATABASE
http://www.sarep.ucdavis.edu/cgi-bin/ccrop.EXE/show_crop_28

...snip.... Root System -- Oat has a fibrous root system (Bugg, pers. comm.). -- Kutschera (1960) reported that oat generally roots to a depth of 84-195 cm and wild oat (Avena fatua generally roots to a depth of 91-160 cm.
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...snip.... scroll down to USES for comments about use as a cover crop.
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...snip....Seeding depth for barley or oat should be no greater than 5 cm (2 in.). Shallow seeding is possible in areas with high soil moisture and leads to more rapid emergence and lessened incidence of root rot disease (Stoskopf, 1985).
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...snip....
Seeding Rate -- Seeding rates are given as 60 to 90 lbs/acre (McLeod, 1982; Miller et al., 1989) and 80-96 lbs/acre (Johnny's Selected Seeds, 1983). Higher seeding rates of oat or barley may be appropriate where rainfall is heavy (Stoskopf, 1985).
\\ Seeding Depth -- Seeding depth should be 1 inch (McLeod, 1982.), and for barley or oat should be no greater than 5 cm (2 in.) (Stoskopf, 1985). Shallow seeding is possible in areas with high soil moisture and leads to more rapid emergence and lessened incidence of root rot disease (Stoskopf, 1985).
\\ Seeding Method -- A firm seedbed prevents frost heaving of the plants from the soil during the winter (McLeod, 1982). Barley or oat are usually planted in rows 15 to 20 cm apart (Stoskopf, 1985). Oat can be seeded into the sod of bermuda grass (Miller, 1984).

What about seeding your oats on TOP of the sheet mulch? They will fall into the gaps, still have enough light to grow, their roots will reach down through the mulch (shaded), and the plants will 'pin' the mulch down to the soil.

Sue

If you seed on top of your mulch those seeds will get enough light, and moisture, to germinate, but if you seed first and then spread the mulch they may not. I have done that with Winter (Cereal) Rye and find that germination is more spotty then if I seed on bare soil.