You can, for a crop should be drilled in, but years ago I questioned broadcasting until I saw it done for a crop here in one of my fields. I've also planted oats for the grass, for deer food plots, inexpensive, easy to do fall season forage. Plow or disc, the soil, broadcast, if not for a crop, broadcast heavy on seed, then disc in, they will come up just fine for grasses. You will have to mow it to keep it going, when it starts to fade to tan, weeds will want to compete. Ideally, under-seeding the grasses, after the oats are disc'd in, if done right, the grasses will come up instead of the weeds. Oats are good at shading out weeds, but as a nurse crop, the proportion needs to be right to do this. My farmer friend always planted his stands of hay like this, oats, with the hay grasses, harvested the oats, then the hay grasses take over. I forget the proportions, but it was done with a grain drill.
After planting the oats, and disc'ng in, this seed being larger is ok, you have plenty of seed to soil contact, but if you broadcast onto a not so soft or worked up seedbed, you will need to roll the area with a cultipacker to get better seed to soil contact for best germination results. If you do the above with grass seed, that cannot be disc'd in, so you disc in the oats, roll once to firm that up, then broadcast the grass seed. Each pass is going to compact and that is something you try to keep to a minimum. Ideally using a grain drill with grass seed boxes, with a cultipacker behind that, essentially making one pass during planting.
Also consider testing the soil for PH and fertility, all of the above is worthless unless the soil is good on PH & fertility.
Photo is a stand of oat grass I planted in mid to late August, broadcasting in a rocky section of the field, technically the power company's land.
