Is it possible to open a large image (20 to 30 GB file size) in ArcMap?
I wanted to know this in advance before doing a project in which I would use UAV to capture very high resolution images and then produce a composite/mosaic final single image.
Yes you can open a large image in ArcMap. I have a TIF that I created for our Emergency Management Office that is 77GB. It works fine in ArcMap (a little bit slow) but it took several hours to create it (necessary for a CAD system). Erica's recommendation about pyramids is a good one. The TIF I have was made from a 4GB SID image. That is a lot of compression. I'd recommend the SID format or something similar (there may be other options).
You don't "import" image / raster data in ArcGIS/ArcMap, unless you intentionally import it in an enterprise geodatabase, which is no longer a recommended practice (if it ever were...). Recommended practice is to store image / raster data in their native format (e.g. TIF,IMG,SID etc), and access them directly, or via building a Mosaic Dataset. An ArcMap document just stores the references to all the data, never the data itself (except things like graphical obects in layouts, but that isn't GIS data). A Mosaic Dataset in ArcGIS is again just a "container" for references to the raw image data, and additionaly provides options for "on-the-fly" fully dynamic image manipulation, like combining bands or changing contrast.
Pyramids are lower resolution copies of the original data, much like zoom levels in tiled map services, just in a format unique to ArcMap, and allow smooth and quick access to large image / raster files. You should create them if they aren't already there. ArcMap asks you to create these pyramids for image data formats that don't have them natively. For image formats that natively have pyramids, like high compression SID, ECW or JPEG2000, ArcMap doesn't create them, but uses the pyramids contained in the image file AFAIK.