Would having a DC-to-DC Step Up Converter Damage the L293D H-bridge IC behind it?
The power (voltage times current) into a DC-DC converter is equal to the power out, plus a bit for inefficiencies and losses, so placing a DC-DC voltage step-up converter either between the Arduino and L293D, or between the L293D and the motors will increase the current drawn from the Arduino.

A DC-DC converter cannot create power - it can only get power from its input, and pass most of that power to its output.