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Yes, you can do that.
Yamaha and Ableton both use 1 through 128 for the Program numbers, so that's not a problem.
But you'll also need to tell Ableton what Bank number to use, and you'll need to adjust Yamaha's numbers to Ableton's numbers.
Ableton has three fields under the "Pgm Change" label, in the box to the left of the MIDI clip's piano roll editor. From top to bottom, these three fields say "Bank ---," "Sub ---," and Pgm ---."
The "Bank ---" field is where you enter the MSB value from the PSR-E403's Voice List, except you'll need to add 1 to Yamaha's MSB value. For instance, Voice No. 007 on the PSR-E403 is "Cool! Galaxy Electric Piano," and its MSB value is listed as 000, so you'll need to enter 1 in the "Bank ---" field.
The "Sub ---" field is where you enter the LSB value, except again you'll need to add 1 to it. For instance, for Voice 007 the LSB is 114, so you'll need to enter 115 in the "Sub ---" field.
The "Pgm ---" field is where you enter the MIDI Program Change #, exactly as Yamaha lists it, except you don't need the leading zeros. For instance, for Voice 007 the Program Change is listed as 005, so enter 5 in the "Pgm ---" field.
When you play back the MIDI clip and send it to the PSR-E403 with those three values, it should play the notes using Voice 007.
