I am using the wordpress transients API to store some commonly used queries throughout my site.
Does this provide any performance gain without memcached supported, enabled, and installed on my hosting?
Is using wordpress transients useless without hosting that supports memcache?
No. You need a plugin that provides some kind of a beneficial effect for transient data to work. However, unlike get_option / set_option, transients can at least be accelerated.
Even without acceleration, what you do get, is some limited form of garbage data collection.