It would not make any difference, unless it was a crappy transformer which would make the situation worse.
Unless your cartridge has more than 4mV output, I'd say to go ahead and try it - maybe with an outboard clip-lead setup - and find out what you hear. The LF cutoff will reduce some rumble and probably tonearm resonances, so it's a balancing act - some good, some risky. See what you hear. To test the worst case, find a record that is recorded pretty "hot" - the overload problem will occur under the same conditions which stress the cartridge's tracking ability, making it difficult to separate them, but if a hot recording sounds good then you are in business!