WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
Building, troubleshooting and testing of these amplifiers should only be
performed by someone who is thoroughly familiar with
the safety precautions around high voltages.
If it is a SE (single ended ) transformer he answer is no since "straightening" the stack will change the gap. IF however the transformer was dropped and this resulted in the miss-aligned stack then it is already screwed up and if carefully done it may help.
If it is a PP (Push-Pull) transformer, the answer is yes.
However, many transformers are varnish dipped and the stack may be glued together. In which case it may be a bad idea.
Q. how did the stack get out of alignment? Was it made this way? Did it get dropped?
I usually just wire wheel them at slow speed, fine sand, and paint them. I don't know what they are from. They appear to never have been used. I got a good deal on them at $400/pr. Shipped. They are 1.5K A-A.
I plan to use them for six KT88 or four KT120s in PPP.
My two cent's worth as an experienced magnetics engineer and manufacturer:
As others in this thread indicate, not worth the small gain you might get for the risk you will take. Unless you can be SURE that the laminations are not varnished or encapsulated in any shape or manner. Typically very unlikely.
The assembly uses what's called "interleaving". Can't tell from the picture but could be 1X1, which means one E one way and then the next E the opposite, with the I accordingly. that's about as good as it gets. The more common 2X2 is still good, if that's what you have.
The fact that there is any interleaving at all says there is no gap in the conventional sense, for that you need a "butt" stack.
If bothered for cosmetic reasons, you might find some sort of plastic or polyurethane or even a sheet of aluminum around the core to cover it up. Don't worry about any magnetic repercussions, there won't be any, unless you have cleaned the edges of the laminations to the point that the insulating layer is gone. If so you can still use an aluminum strip to dress the edges but you'll have to provide a little insulation to make sure you are not shorting out the stack and degrade its properties. If the transformers are thermally close to the edge, paint them with black varnish (thin, in other words) and call it done.