I am using some polygons and rasters whose initial extents cover all of Canada or all of North America. I am interested in a small area in Ontario that is in UTM zone 18. I would like to use the UTM 18 projection for this project. If I convert all of my layers into WGS84 UTM 18 using ArcGIS, obviously the parts of the layers outside of the UTM 18 zone will be horribly distorted. I will be cropping the layers after to only my zone of interest once they are all in the same projection. But will the part of the map that is actually in UTM zone 18 be distorted as a result of the reprojection of the entire span of Canada, or will this part be fine?
Everything should be fine:
For only showing an area in the UTM zone 18, you can easily zoom into your area. (One additional hint: Use Bookmarks [Menu bar, Bookmarks, Create Bookmark] to keep your selected view even after working with some Layers.)
ArcGIS will project any Layers 'On the Fly' into your desired projection. If you don't want to do any calculations with your rasters, even reprojecting them shouldn't be necessary. Same for the Shapefiles.
The only disadvantage I have experienced with this 'easy way' of visualising is that large/detailed Shapefiles far outside your mainly projected area are processed relatively slow while ArcGIS renders them to show them on the screen.