Doesn't look like it, unless you are OK with 2G.

Jolla's device supported frequencies:

GSM: 850/900/1800/1900 MHz
UMTS: 900/2100 MHz

AT&T mobility, USA: (from here https://en.wikipedia.org/wiki/AT%26T_Mobility#Network).

GSM/GPRS/EDGE: 850 MHz, 1900 MHz PCS
UMTS/HSPA+: 850 MHz CLR, 1900 MHz PCS

Which means, 2G would probably work, 3G - no. LTE isn't clear, since we don't know what frequencies the device supports, and it's not enabled in software yet anyway.

Basically with T-Mobile is the same story. 2G would work, but nothing else so far.