Yes you can. That's how many (most?) astrophotos are taken. For terrestrial use, using a newtownian reflector would be awkward, but refractors, SCTs, and Maks would work fine.
Most telescopes have curved focal planes, so you might need to add a field flattener (or reducer/flattener) for best quality results, but there are some telescopes designed as astrographs (scopes for taking images) that use designs that give you a flat focal plane.
One example of this are Takahashi's FSQ106ED scopes - a flat field 530mm f5 astrograph refractor, corrected out to near IR and UV wavelengths, with a huge 88mm native image circle, with optional extender to take it up to around 840mm focal length at f8 (with a 44mm image circle big enough for full frame)
I've read of at least one professional wildlife photographer who uses one - it's a fairly hefty setup to cart around, but (as usual for tak) the image quality is excellent.
Here's a central crop of an image (of a Bluetit in the UK - they're small birds, about half the size of a sparrow) I took with a FSQ106ED and extender at 840mm / f8 with an APS sensor Nikon D300.
and here's the full image:
So you can see that if you can live with manual focus, it's certainly a possibility. You can also use less expensive telescopes - but there are some potential quality issues with some of the cheaper achromatic refractors, since they don't have as good colour correction. But if you already have a scope with a 1.25" or 2" focuser, it might be worth getting a T ring and suitable nosepiece and give it a try (You can also barlow lenses (the astronomical equivalent of a teleconverter) threaded to take a T ring, and more or less double your focal length that way.
With my Nikon, I still get the focus confirmation light when focusing manually with a non-electronic lens- I think Canon's may need an adapter to enable this.