Is it possible to attach a picture file in a Rich Text field and have it displayed in another in a Notes client?
I assume you mean, in a program. Not easily, no.
It's not clear whether you want to create a file attachment and have someone else be able to view the document and see the picture that's in the file, or whether you want to import an image file (as with the File/Import menu) so that there is no attachment and the image is just there in the Rich Text.
The redbook Domino Designer 6: A Developer's Handbook contains a chapter on programming Rich Text, which includes a discussion of how to create Rich Text by importing HTML in the front end. This would let you include an image, but it doesn't operate quietly in the background -- it does stuff on the person's screen. Alternately, check out the Midas Rich Text LSX from GeniiSoft.com or look into using the Notes C or C++ API.