The spatial resolution depends on the bandwidth of your transmission. An infinite-bandwidth signal is a delta in time, and gives infinite precision. Any finite bandwidth impulse will be a sinc in time, with temporal width proportional to the inverse of the bandwidth. So a higher bandwidth impulse will be shorter in time, which would give better temporal resolution.

Typical radar works by sending and receiving a high-bandwidth impulse, which requires high-bandwidth transceivers. Let's say that transmission occupies frequencies between f0 and f1. SFCW radar works by sending a bunch of individual low-bandwidth transmissions between f0 and f1. So each transmission is small, but together they occupy the same f0 to f1 bandwidth. Assuming the environment didn't change in the time it took to send all of those low-bandwidth transmissions, you've effectively simulated a high-bandwidth impulse using a bunch of low-bandwidth impulses. So the spatial resolution will be the same.