Absolutely, and you can just buy a 230v replacement (http://www.marshalljmpmodshop.net/miscellaneous_parts_and_replacement_tubes.htm) which is less expensive than the MDRT. BTW if you go this way, get one from MJMP, some other replacement trannys can have issues and break down over time. In MJMP I trust....
However, the MDRT not only works on either 110/240v it improves the sound of your MP1. (from MJMPs site; The MDRT is a 24VA transformer which can deliver 12.6V to the heaters. The high voltage has gone up to 240Vdc / 8mA. The original is only a 12VA transformer, and will only deliver between 8 and 9 V to the heaters and the high voltage is 190Vdc / 4mA. So the MDRT will enhance the sound, producing better low end, less noise and the sound will sound less compressed.) which is why I would go MDRT (but it does cost more)