Will i be allowed to continue my recruitment process on a T2 visa?

Hello,

Yes you can apply and continue to join under a visa. It is important to understand that until the day you join, you're responsible for making sure that your visa is valid and you're in the UK legally. If your visa runs out, you will need to pay for yourself to go back home to apply for a new visa, before carrying on with your application.
You'll be given 'exempt immigration control' status while you're serving. If you want to stay in the UK after your service ends, and have served for six or more years or been discharged as a result of an illness or injury caused by your Service you will not have to pay a fee.

The above can be found on the Army Jobs website here: https://jobs.army.mod.uk/how-to-join/can-i-apply/nationality/, as well as a link to the UK government page on Visa fees.