Welcome to the forum puckett. To update the firmware, you need to copy a file from Tascam's website to the sd-card, then turn on the machine in a special way. You can copy the file using any method you like, via a USB link or by physically plugging the sd-card into any device which can write to it. So if your Android phone has either of these features, then yes.
I can't guarantee it will work - you'll just have to try it. If the phone detects the dp24's card as an external storage device - like a memory stick - then you're in with a chance. Instructions for upgrading are on Tascam's website... or in my step-by-step guide - sorry, unashamed plug ... along with the firmware itself, so it will tell you where to copy the file. Once you've done this, make sure you un-mount the card from Android before disabling the link from the dp24 end. Good luck.