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Hi there, it's certainly possible.
You can see an example on my site :
Hyogo AJET It's a site for English teachers in Japan.
Basically, the random image option comes as a MyAlbum-P block called 'Pic Up Photo' You'll need to make it visible in Admin>System>Blocks and also set group permissions to view the block in Admin>System>Groups.
Moreover, if you click the 'edit' link in Admin>System>Blocks you can set the Category you'd like to display photos from and choose whether to include sub-categories or not. You can also set the maximum width for the image and the change-cycle of the image in seconds.
I like MyAlbum-P
hope this helps,
David Thomas.