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I have a hybrid bike with front and seat post suspension. It's easy to see how front suspension reduces pedaling efficiency by using some of the power for compressing the shocks, so I keep it locked on paved roads.
In situations where performance is more important than comfort, does a suspended seat post cause any harm to end results? I.e. would I get better times / speeds with a rigid saddle post?
Seat post suspension is not designed for efficiency.
It is designed to add comfort to a hard tail mountain bike frame. There are only a few really good suspension seat posts, and they are rarely used on hybrid bikes. Almost always, you will find that the suspension post on a basic hybrid is just a spring in a tube.
Occasionally, they add the ability to pre-load the spring to make it feel stiffer, and that is a slightly better option.
On that type of suspension post, you affect your efficiency when the post is active because your seat height will change as you ride, and as the post compresses. This will change your position and leverage, and usually, not for the better. It will detract from the amount of power you are getting out of the system, while still using the same or more energy to put in that power.
A true full suspension will account for most of these factors, and is therefore generally a more efficient choice, but weight, cost, and designed riding style for a bike will also affect the efficiency.
To directly answer your question, yes, you would be more efficient without a suspension seat post, assuming all else was equal.
However, most hybrids are lacking in any number of areas in regards to efficiency, and you may not feel the actual difference in efficiency from the seat post given the bike you are riding.
Note that, in theory, suspension of any sort saves energy on a rough surface, since you "burn" less energy moving your own body up and down as you go over bumps. The negative side occurs, however, if the suspension absorbs energy as the pressure changes as you pedal -- ie, it goes up and down with each pedal stroke.
Again, in theory, a seatpost is least likely, of all suspension types, to "go negative", since when you're pedaling hard most of your weight is supported by your legs, not the post.
But the devil is in the details, and it's hard to predict what happens in "real life". I suspect that to some degree the simple fact that your seat height is constantly changing can "throw off" your stroke -- not absorb energy per se, but make you less able to produce energy efficiently.
In asking, you should specify whether you use cleats or not. When riding with cleats, and while sitting, you - at least I - use the seat post as counter leverage. In these cases, you will put part of you work into the seat post's damping. Without cleats, I see little proof that damping, probably accompanied by variation in position and corresponding levers, necessarily costs more energy. If this is the case, I like to see at which position in the cycling movement where this is the case.
A doctor from the German Sports University Cologne made some tests in laboratory and realized the suspension helps. A study was made at Saint Cloud State University, this time it was off-road. The result answers your question.
Riding a front suspension bicycle resulted in faster finishing times in a cross country time trial versus a rigid bike in a second part of the study
You can read more about this two studies here. One relevant quote is: "The suspension seat post was surprisingly efficient with a 25 percent reduction."
