You may find the results somewhat lacking. Those transformers are a long way from being the best thing in the world for quality, but they are at least somewhat adequate for mic levels (-50dBu). When you start running line levels through them (-10dBu or thereabouts), you'll find that they saturate badly, and their frequency response will get even worse. It's worse yet if the output buffer of your synth has a little DC offset, and runs DC through the primary: that'll partially saturate the core with a DC_fixed_ magnetic field, and lead to asymmetrical distortion (munging positive-going peaks worse than negative-going, for example).
Now, on the other hand, you may _like_ that distortion! I once built an iron-munger box for a keyboard player- it had a pretty decent Ampex input transformer in it, and a nice 6v supply, and a pot that let him just _cream_ the primary with DC: twist the knob increasing the DC bias, and the output level would drop, the signals would get hideously munged, and generally all hell would break loose.... Sounded like dogmeat, but he liked it to add "character" to his
Prophet-5. There's no accounting for taste...
Mic-level impedance matching transformers, and line-level impedance-matching transformers, are different kettles of fish. The winding and core designs do differe depending upon the designed operating levels. By all means try it, but be prepared to be disappointed...
Unless you have a long signal run, there's probably not much reason to concern yourself with going balanced from the keyboard output. Are you dealing with noise issues here, such as ground loops (which using a DI would certainly help), or is this just something you want to do because it is often recommended as "better"? For a short run from a bank of keys to the local keyboard mixer, it may not be worth the expense. What problems are you trying to solve?