You don't need to do that for printing. White is not reproduced as a separate colour in most printing processes, including regular screen printing, unless you have a specific need for it.
If the pen and ink drawing is monochrome, a screen can be made that will print in black ink, or any other single colour of ink. The white areas will be transparent.
If the drawing is coloured, it can be reproduced in CMYK printing - again no white ink is involved in the process.
As to answer your question directly, it is possible to remove a white background should the need arise. In GIMP click Colours > Colour to Alpha > OK - then export in a format that supports alpha transparency, such as PNG, GIF, PSD, TIFF, XCF.