...Like said, we have seen probes capable of that: TNG features several shots of probes being flown out of the forward torpedo tube at crawling speed, but soon transmitting information from far, far away. And then there are the shuttlecraft: not that
much smaller than a torpedo, but (seemingly) capable of going to distant stars and back. So we'd probably have to provide an explanation for why a torpedo-sized machine could not
go to warp all on its own.
The problem with "The Emissary" is that the probe is among the smallest we have ever seen; is shown to be mostly empty inside; reaches exceptionally high warp speed; and sustains that speed for a long time.
We may limit the problems with that by saying that the probe we see is just the last stage in a multistage system, and that it uses the powerless coasting trick from "Force of Nature", and so forth, but the sum total of the problems is still rather overwhelming.