Publisher does a lot of things. It is a large add-on that brings a massive feature set, therefore, it will add to the page load time of your sites. It is difficult to say exactly how much time it will add because it depends on what features you are using and what 3rd party add-ons you have installed. For this reason, it is recommended that you have some sort of caching strategy for your site (even if you are not using ExpressionEngine or Publisher, you should have some level of site caching). Fortunately, we also offer a fully featured caching module called Speedy. Publisher has a lot of built in caching as well. For example, the first page load after saving an entry may take additional processing time and queries because it will be re-generating some caches.
Publisher 3.x comes with built in bench marking. If you have the Output Profiler enabled on your site. Below is an example of the bench marking output added to ExpressionEngine's Performance tab in the Output Profiler. As you can see you in this example, the full page took 14 seconds to create an un-cached page, but only 3.2 seconds of it is the result of Publisher's hook calls and other processing.
Memory Usage: 34.9MB of 256MDatabase Execution Time: 0.6418Publisher Session Start: 0.1550Publisher Core Boot Hook: 0.6321Publisher Core Template Route Hook: 0.0586Publisher Channel Entries Query Result Hook: 0.0081Publisher Assets Data Query Hook: 0.0038Publisher Relationships Query Hook: 0.6546Publisher Channel Entries Tagdata Hook: 0.0041Publisher Translate Phrase Tag: 0.0004Publisher Languages Tag: 0.0234Publisher Category Entry Translations Tag: 0.0168Publisher Languages Tag #2: 0.0193Publisher Translate Phrase Tag #2: 0.0004Publisher Languages Tag #3: 0.0192Publisher Languages Tag #4: 0.0277Publisher Translate Entry Tag: 0.0456Publisher Translate Entry Tag #2: 0.0394Publisher Translate Phrase Tag #3: 0.0005Publisher Languages Tag #5: 0.0191Publisher Languages Tag #6: 0.0283Publisher Channel Entries Query Result Hook #2: 0.0152Publisher Grid Query Hook: 0.0012Publisher Channel Entries Tagdata Hook #2: 0.0014Publisher Channel Entries Query Result Hook #3: 0.0742Publisher Channel Entries Tagdata Hook #3: 0.0033Publisher Channel Module Categories Start Hook: 0.3291Publisher Channel Module Categories Start Hook #2: 0.0422Publisher Channel Module Categories Start Hook #3: 0.0582Publisher Channel Module Categories Start Hook #4: 0.0498Publisher Channel Module Categories Start Hook #5: 0.0424Publisher Channel Module Categories Start Hook #6: 0.0567Publisher Channel Module Categories Start Hook #7: 0.0744Publisher Channel Module Categories Start Hook #8: 0.0480Publisher Translate Phrase Tag #4: 0.0004Publisher Translate Phrase Tag #5: 0.0006Publisher Translate Phrase Tag #6: 0.0006Publisher Translate Phrase Tag #7: 0.0004Publisher Translate Phrase Tag #8: 0.0004Publisher Translate Phrase Tag #9: 0.0004Publisher Translate Phrase Tag #10: 0.0004Publisher Translate Phrase Tag #11: 0.0004Publisher Translate Phrase Tag #12: 0.0004Publisher Translate Phrase Tag #13: 0.0004Publisher Template Post Parse Hook: 0.0056Publisher Total Execution Time: 3.2234Total Execution Time: 14.3696