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 256M
Database Execution Time: 0.6418
Publisher Session Start: 0.1550
Publisher Core Boot Hook: 0.6321
Publisher Core Template Route Hook: 0.0586
Publisher Channel Entries Query Result Hook: 0.0081
Publisher Assets Data Query Hook: 0.0038
Publisher Relationships Query Hook: 0.6546
Publisher Channel Entries Tagdata Hook: 0.0041
Publisher Translate Phrase Tag: 0.0004
Publisher Languages Tag: 0.0234
Publisher Category Entry Translations Tag: 0.0168
Publisher Languages Tag #2: 0.0193
Publisher Translate Phrase Tag #2: 0.0004
Publisher Languages Tag #3: 0.0192
Publisher Languages Tag #4: 0.0277
Publisher Translate Entry Tag: 0.0456
Publisher Translate Entry Tag #2: 0.0394
Publisher Translate Phrase Tag #3: 0.0005
Publisher Languages Tag #5: 0.0191
Publisher Languages Tag #6: 0.0283
Publisher Channel Entries Query Result Hook #2: 0.0152
Publisher Grid Query Hook: 0.0012
Publisher Channel Entries Tagdata Hook #2: 0.0014
Publisher Channel Entries Query Result Hook #3: 0.0742
Publisher Channel Entries Tagdata Hook #3: 0.0033
Publisher Channel Module Categories Start Hook: 0.3291
Publisher Channel Module Categories Start Hook #2: 0.0422
Publisher Channel Module Categories Start Hook #3: 0.0582
Publisher Channel Module Categories Start Hook #4: 0.0498
Publisher Channel Module Categories Start Hook #5: 0.0424
Publisher Channel Module Categories Start Hook #6: 0.0567
Publisher Channel Module Categories Start Hook #7: 0.0744
Publisher Channel Module Categories Start Hook #8: 0.0480
Publisher Translate Phrase Tag #4: 0.0004
Publisher Translate Phrase Tag #5: 0.0006
Publisher Translate Phrase Tag #6: 0.0006
Publisher Translate Phrase Tag #7: 0.0004
Publisher Translate Phrase Tag #8: 0.0004
Publisher Translate Phrase Tag #9: 0.0004
Publisher Translate Phrase Tag #10: 0.0004
Publisher Translate Phrase Tag #11: 0.0004
Publisher Translate Phrase Tag #12: 0.0004
Publisher Translate Phrase Tag #13: 0.0004
Publisher Template Post Parse Hook: 0.0056
Publisher Total Execution Time: 3.2234
Total Execution Time: 14.3696