ISRC codes, yes. UPC codes, no.
Gramex has assigned Anti-Joy a registrant code to provide every song you upload with an ISRC. It's free and automatic.
If, for any reason, you wish to use your own ISRC codes, it is a simple process. All you need to do is select "Already have your own ISRC codes?" below the audio file section in the upload form.
There is no way to specify a custom UPC code.
If you want to apply for a UPC issued by GS1, please contact your local GS1 office here.
If you prefer to purchase your own ISRCs, visit https://www.usisrc.org/