NO.
Its a recipe for disaster. Imagine: your barrelling down the DH run at Cwmcarn, come over a blind jump you know well, safe in the knowledge that nothing is coming the other way & nobody is going to be hanging out on the downside of a jump (cos its **** dangerous) & whoops whose in your landing zone but Shep who gets taken out by 190+ lbs of rider & bike going over 30mph..
End result: not good, a seriously injured (perhaps dead much loved companion). A biker who will probably have a trip to the local A&E at the very least. Not too mention the associated legal fallout that would come from such an accident.
Its a very selfish person who thinks that outcome is a risk worth taking.
If you do want to go ride with your dog – do it somewhere ELSE, not on bike specific trails. Whats wrong with using a bridleway WHEN you know that other users are at least 1/2 expecting something else around the corner.
I dont want to have to be thinking about the possibility of somebodies mutt being around the corner the next time Im flying down Whites Level!
ps I love dogs – have lived, loved & buried 5. And still counting..