This question might be strongly opinion-based, but I also think it might be interesting. I know there is a guide for Lego builders to decide if their build is legal or not. However, the cases of this guide focus on assemblies where the final configuration has some issues with friction or internal stress. But at the same time, there are assemblies, which do not deal with either of these, except at the moment when they are put together. Here is an example:
The answer depends on your definition of "legal". In the strictest sense, it means "can be used in official LEGO sets", and in this case, this is definitely not legal, as the axle is not designed to bend that way, unlike the many various hinge and joint pieces.
On the other hand, "legal" might mean "does not cause damage to the pieces", and in this sense it is a borderline case, as you can see the end of the axle retaining its slightly bent shape, but it's nothing that couldn't be fixed with a little more force applied in the correct place and direction.
Whereas on the far end of the legality spectrum, the status of any technique or piece is subject of individual opinion or decision. You are certainly free to employ any combination of parts, use 3rd party parts, paint, glue or cut pieces to your heart's content and shouldn't fear any reprisal from the LEGO Police. Collections curated by others, events or competitions might (and often do) apply a restriction on at least a subset of these, so if you are not in the position to judge the legality, it's best to directly ask those who are.
EDIT based on Michael's comment:
Another criterion in the definition of legality is often "can be easily taken apart by a child", which this design is clearly not.
From LEGO point of view this definitely would be illegal to assemble such axle with particular frame since you cannot build and then take this apart without bending the axle.
But from AFOL's point of view this could be a doable solution for a MOC if there is a real need. There's plenty of space to bend the axle and it won't get damaged.