My bicycle went from this when I bought it:
To this when I crashed (note the front fork bent where it attaches to the stem; front wheel almost touches the down tube):
Well, that second image is a little too small to see what the bike's condition is, but I knew a guy back in the 70s (a fairly avid biker) who bent his fork rear-ending a parked car. (Yeah, he was a bit sheepish about that.) The fork was bent back to where the tire just barely cleared the down tube. He rode it like that for at least 4-5 months, probably doing 200 or more miles a week.
(Note: This was a steel bike -- if that wasn't obvious from the date.)
Clearly, handling will be affected -- that's for you to assess. And I wouldn't trust a bent fork with aluminum or composite components.
Good LBS can straighten steel fork, but it would be a good idea to replace it when you can.
But in your picture top tube also seems to be bent. If that is true than the frame has also been compromised which is much more serious problem.
besides the structural issues, looks like this crash has changed your bike geometry rake, head angle, tail, and wheel base. This will likely result in much more sensitivity to handlebar input.
If you can, I would advise against riding the bike, particularly on low traction surface since a small jerk can put it a handle-bar lock and you into an endo.
As others noted, the clearance from the down-tube is also cause for caution. The steel fork can likely be bent back, provided that there are no frame fractures and wheel damage (hard to imagine the wheel being perfect with forks bent).
otherwise, it doesn't seem likely that the steel bike would disintegrate as you're riding.