That's unlikely - because the sync speed is not passed back to the Home Hub.
Ah, I was talking about ADSL, since the OP postulated an ADSL speedtester ported forward to FTTC.
Do we actually know that the BT Retail speedtester, that I was commenting on, works on FTTC and does report sync speeds for BTr custs?
I'm with you now. I based my answer on the BT Openreach documentation and packet traces I've examined of what happens with FTTC on my line.
On FTTC, the subscriber end doesn't get the synchronisation speed passed to it by the DSLAM in the cabinet (a shame, otherwise I could add it to my logs), and the BT Openreach modems are normally locked in such a way to preclude the subscriber from reading sync speed and other technical data out of the modem. There are now known ways to access technical data on both types of modem, though I believe there's still some issues with gaining access to the newest version of the ECI modem.
If the BT Retail speed tester or the Home Hub knows FTTC synchronisation speeds, this data is most likely coming from the BRAS, or is coming from periodic monitoring reports about end user circuits passed to BT Retail by BT Openreach via BT Wholesale (in this case, BT Wholesale are BT Openreach's customer - BT Retail are BT Wholesale's customer).
Zen make a synchronisation speed history available via their customer portal. Other ISPs often have similar 'self help' solutions to get hold of data about your line.
On BT Retail ADSL, the DSL modem is in the Home Hub, which therefore has access to the key line parameters.