Wiring Ethernet through Telephone Cable
Nope! Plain Old Telephone Service (POTS) jacks were usually daisy chained as you describe. Ethernet requires a &quot;home run&quot; from each jack to a modem, router or switch. Also, it's probably cat-3 which is unsuitable for Ethernet.
EDIT:  Based on comments (which sometimes go away, but answers don't), I'm adding to my answer here:  According to others Cat-3 can be used for limited ethernet service (I wouldn't recommend it), but every jack would have to be wired in a home run configuration, which is uncommon for POTS wiring.   Next:  As others commented, the POTS wiring might not even be Cat-3, it could be 4 wire cable (Red, Green, Yellow, Black) which was very commonly used back in the day, which wouldn't work at all.