Yep, you can have the bath at room temperature when you put your frozen food in. Depending on what you're cooking and how long it takes for the bath to come up to temperature, it may not impact your cooking times.
(obviously, if you displace half of the volume of your vessel with frozen food, it would take some time to come up to temperature - certainly in that case, I'd preheat the water first)
One great thing about sous vide is being able to reproduce your results every time. The more you keep the cook time / temperature precise, the more your end result will be identical.