About to start a new project I have some questions before I start
Without knowing the inverter specs and with how non steady the current is on color changing leds we can't tell you how inefficient the setup will be, but it will probably be significant considering you are using a drill battery.

Yes. Very much so. Both seem to indicate they use an external AC to 12V DC adapter, to a barrel jack. You can use a switching regulator to bring down the 18v (nominal) to a steady 12V. 11V may be better for a minimal brightness hit but will let the leds live longer. You may also want to get a low voltage lockout circuit so you don't over drain the battery.


You want to check the actual voltage the ac adapter puts out (measure, or just trust the label). The images on the first one indicate it is a single IC per segment and that tends to indicate a 5V led. So be certain.