SUPPLYING 24VDC TO A 24VAC INPUT THAT GETS RECTIFIED. AN ISSUE?
Do you really mean to "SUPPLYING 24VDC TO A 24VAC
INPUT.."? Then, you can't use the transformer any longer.
A better way is to parallel your new DC supply to the DC side of the original power supply, but, also serial a diode in you new DC supply to prevent back charging the new supply. In this way, you can have both supplies on at the same time or individually. Even if you are getting rid of the transformer permanently, this is still better, though you do not need to serial the diode now.