Personally, I think you will be fine. Quality adhesives are so good
these days I don't always use a mechanical fastener if I have the time
to glue and clamp.

By using adhesive only, you don't risk the chance of splits from
fasteners, and errant nail sticking out of your project, you don't
have nails to fill, etc., so you can cut down the time spent overall
when assembing and finishing.

If you are thinking you need a mechanical fastener, try doweling or
using biscuits (don't make me haul out the furniture manufacturer's
study that showed the added strength to the joints...) or maybe a
pocket screw in an inconspicuous place.

Try not to overglue as the residue or cleaned areas can affect
finishing. Use the correct solvent to clean up while the glue is
wet. I used to wait until the glue was dry and clean up with a sharp
chisel. However, after slicing through too many micro-veneered panels
of birch, I clean TB with a damp sponge.

As always, just my 0.02.

Robert