"Fare splitting or "ticket-splitting" is when a passenger buys multiple tickets for two or more separate legs of a single journey, instead of just one ticket"
Yes, you can upgrade with Seatfrog if you've booked a split ticket, providing you have valid tickets from your departure station to the destination station. To bid for an upgrade you will need to add the full trip to your Seatfrog account, and not the separate legs.
The only time you would need to add separate legs is if you needed to change trains. If a change is needed then you will need to add each train to your account and bid in the separate auctions. For example, if you were travelling from Edinburgh to Kings Cross and you'd purchased split tickets travelling on a single train; one ticket from Edinburgh to Newcastle and another from Newcastle to Kings Cross. You would just need to bid on an upgrade for the length of the journey, from Edinburgh to Kings Cross.
If you need to change trains at any point, let's say at Peterborough, you'd need to use Peterborough as the destination from Edinburgh - and the origin to Kings Cross.