As the first poster said, if there is a stuck 
douga, it is usually easily removed. But, yes, 
only at the sacrifice of the douga. Since a 
matching douga is a plus for a lot of collectors, 
losing the douga could effect the value a little 
bit. I pay more for dougas - I love them!! ^_^ 
(Although, I don't pay more for a stuck douga 
because of A. problems with removing it and B. I 
don't like things stuck to my cels.)

But the basic value of the cel *is* in the 
character, the pose, and the position. A well-
posed cel of a desireable character that lacks a 
douga will always be worth more than a poorly 
posed cel of that same character - or a cel of a 
less desireable character, no matter if those 
cels come with the douga or not.

(There are some exceptions to this rule, mainly 
with series where it is exceptionally rare to 
find a matching douga - but I don't think this 
applies to Dragonball. . . ?)

In the case of a stuck background. . . That's a 
bit more problematic. Many collectors would 
consider it a detraction if the stuck background 
were not the matching one. Also, in some cases, 
it is possible for the paint from the background 
to seep into the cel paint and create a "stain" 
that can be seen from the front of the cel. Also, 
given the heavier weight of the paper the 
backgrounds are painted onto, there is more risk 
of damage to the cel when trying to remove it 
from the background. Stuck douga I'll give or 
take, but I usually try to avoid stuck 
backgrounds.

On a completely separate topic (since I don't 
know if you watch Dragonball with your nephew), I 
think that there is a low incidence of matching 
backgrounds with Dragonball cels. Correct me if 
I'm wrong, people - but doesn't Dragonball suffer 
from Sailor Moon's fate in that respect? (Do all 
anime from that studio wind up with mixed 
backgrounds?) Anyhow, I don't know if this matters
to you or your nephew, but it's something you 
should know in any case.

Happy hunting! ^_^  (And I'm sure Dragonball fans 
will be interested. . . What character are you 
looking for? ^_^)

Many Sharp Smiles,
--Drac