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.
I had a 80's 10 speed with a similarly bent fork. It was also akimbo to the right, but not so much you could see it with your eyes.
Handling was... interesting. It rode okay but hit any sort of a bump and the bike wanted to turn right into the traffic lane (we ride on the left.)
I only figured out the fork was misaligned when for some reason I held the front wheel nearest the downtube and the downtube in one hand, forcing them to be in-line. The front of the wheel was visibly pointing to the right by a couple of degrees.
Once we'd noticed that, other evidence was noticed. The bike's two tyre tracks were side-by-side when riding straight ahead.... the back tyre followed about half an inch to the left of the front tyre's track.
I'd seen paint cracking and frame rust about 1 inch astern of the head tube, on both the top tube and down tube. Once I dismounted the fork, the internal part of that showed a subtle bend as well.
I fixed it using brute force, some pipes for leverage, and a stout bench vise. Testing was done on a flat concrete patio using rulers to measure the height of the fork crown from the flat concrete, and a length of string to measure from the fork crown "shoulder" to the opposite-side dropout.
After reassembly, the bike was much better to ride, and I got a peak speed of 48 km/h.