you cannot see this small difference directly in PAG or agarose but if you can find another restriction enzyme that cuts the plasmid and insert into smaller fragments it should be possible to distinguish inserted and non inserted as well as between your fragments by the digestion pattern using either type of gel

The 3'UTR that you have typed out is pretty short, so I would first check that the oligo that you had synthesized properly lines up with the full 3'UTR of your gene of interest using genome browser or something.

I would then check on the size of your purified, synthesized oligo to determine where it would show up on an agarose gel or page, depending on which would suit the size of your fragment. Then, after cloning, you can do a double digestion and single digestions of the plasmid. You should see only one band the size of the plasmid for single digestion (e.g. XhoI only, or SacI only), but in the double digestion (XhoI+SacI), you should be able to see a band of a much smaller molecular weight that corresponds to your insert. When I did cloning for pmirglo, the insert was pretty clear in the double digestion. It should be possible to go down to as small as 50bp with the right gel and running conditions.

In general, you can only detect a difference of 10% or greater in DNA fragment sizes on an agarose gel. So, no, not with a standard agarose. Order the damn primers and check using PCR. Or look for another restriction enzyme.

Thanks for answers. I decided to double digest my plasmids after transformation. That way, if the insertion is occured I would see 80 kb fragment. So probably I will handle with this way.

Thanks for people who adviced me to use digestion method.