Yes, you could use either drawString() or pack all of the characters into a single char[] and use drawChars(); it's up to you. You set the font on the Graphics before drawing the first letter, and go from there. If you can calculate the correct points for the gird lines, doing the same with a slight adjustment should work for the characters.
I recommend experimenting with it a little and see how far you can get. Come back if you get stuck and post what you have with some specific questions.
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