Yes, if you can load a particular image format you can save it too as long as you add the file extension (so Darkbasic Pro knows what format you want it to use). PNG is the most useful image formats to use so it's definitely in the list of formats we can save despite the help files not mentioning it.
Run this and check the directory you ran it from:
` Make a box
box 0,0,screen width(),screen height(),rgb(255,0,0),rgb(0,255,0),rgb(0,0,255),rgb(255,255,255)
` Grab the image
get image 1,0,0,screen width(),screen height(),1
` Save the image
save image "TestBackground.png",1
wait key