Its a gamble. theres no guarantee you are going to get a TC or that they will sponsor you. You dont give any details.
Some firms might retrospectively pay, but others will not.
I dont think it greatly improves your chances, unless ofc you get stunning grades.
I would try and get experience or improve my cv as well as put a lot of effort into my applications.
Whilst uts understanable you are keen, you should also be patient and determined as many people dont make it. The important thing is that you get to your destination eventually rather than never.
If you self fund the GDL, then will you be prepared to self fund the LPC as well? Some people do and still dont get TC's.