Hi,
TTL lasers can only be turned ON (generally 5v) or OFF (0v) only. Analog lasers can be turned ON (generally 5V), OFF (0v) or partially on (anything between 5v and 0v). In this sense yes, you can use an analog laser controller (i.e. the LaserShark) to drive a TTL laser.
OpenLase has an option to only turn the lasers on/off too (In the Laser output configuration app, look under Color settings).
If you are asking if the LaserShark will be able to dimm your lasers (possible by turning the laser on/off at a frequency much higher than the galvanometer kpps rate to "fake" dimming), then no the LaserShark cannot do this. Generally if you look at the specs of TTL lasers (i.e those from ebay) they are only rated for 10khz which is much slower than the galvos thus making dimming impossible anyhow.