Yes. SlideDog uses your installed version of PowerPoint to display your slideshows. The slides, animations and videos will look the same as if you would open and run the slideshow manually through Office PowerPoint.
But on a general note, presentation files may not always act and look the same on different platforms and versions of presentation software. For example, a .pptx file made with special effects only available in PowerPoint 2019 will not look the same when viewed in PowerPoint 2016. You should always check your presentation files in advance on the computer you intend to use for your live presentation.
Another rule of thumb is that you should always embed external resources when possible. For instance, if you try to show a PowerPoint with non-standard fonts without embedding them or making sure they are installed on the target computer, independent of SlideDog, the text might not be shown correctly.