I tried that once, not straining the primary, though I took it another step further: I never strained that batch at all! I ended up racking it about 3 times in a row trying to leave all the floaties behind. I don't know whether I aerated it more doing it that way or if I should've just strained it like I was otherwise going to.
Since then, I came up with another plan: sanitize a cheesecloth, and stick it around the end of your siphon that goes into the primary. That way it gets filtered before it even gets siphoned. Of course it won't get your beer crystal clear, but it should keep the floaties out.