I never use hops bags, and I usually don't strain my wort unless I have a ton of gunk. So far (200 or 250 batches), so good.
Yours will be fine. There isn't any reason to worry about hops or break material (that crud that comes from cooling the wort- it's coagulated protein) in the fermenter. It'll all settle to the bottom with the flocculated yeast in the end, anyway.