No. Those front axles are pretty much the same width, and I believe the brakes and wheels all assembled will be very similar too. The '37 rear may be an inch or two wider than an original A, but still shouldn't rub fenders unless you put really big rubber on those wheels.
another.... IF using a stock undropped 32 heavy axle, with stock 37 spindles stock a crossmember BUT reverse eyed spring then using a stock 40 steering box cross steer and stock unsplit wishbone, will the drag link hit the pan on an 8ba IF using the same height tyres, will the frame be nose up it cant be can it. 32 axle is 1.5'' lower than an A reverse eye spring is another inch?
I can't answer about the height issue, but yes some 40 backing plates will bolt onto the 37 spindles. Actually 37 spindles are exactly like 40 spindles.
Are his 37 mechanical brake drums the same as 39 Hydraulic brake drums though? That is the question he needs the answer to. I was thinking about running wide 5s on my 31 Vic before I sold it and never researched that answer. My made back when using T rails Tear drop trailer frame has wide 5 rims on it. I'd still like that look on the T modified that I will most likely build with the parts I didn't sell.