Not a problem although it won't get that glaze.
You could certainly cook it like that then stuff it
in the oven with some brown sugar at the last.
I'm trying "drunken Turkey" this year , got a young
turkey breast and a large can of Foster's Lager, pop
the top, but the breast over it, place in a aluminum
pan on the grill cover with foil and cook, remove foil
for last 30 minutes and baste with juice.
Will let you know how it turns out.
And Remember......ALWAYS REMOVE THE GIBLETS FIRST.
my sister didn't pay much attention growing up, so
the first one she did on her own, well you know the story.
you won't remember eating it!
I do like the glaze. I will be willing to glaze it at the last. :-)
Hope the turkey turns out well.