If you were to ask this question a few decades ago, I would have given you an unmistakable "yes" because then, pretty much everything you "read" is a book, or a book-like object. Magazines, novels, brochures, manuals ... etc., can all be loosely classified as "books". So 看书 cancould be a generic term for reading.
Fast forward to the 21st century. 书 (books) come in all shapes and forms. You can read a printed book, or a digital book (on your computer, ipad, or even your cell-phone). So when you say someone is reading, s/he can be actually be holding a printed book, a cell-phone, a laptop etc. If you know that person is, in fact, reading, then sure, you can say 他在看书.
But then, a person holding a cell-phone or iPad can be watching a video or doing other things as well. If you don't know what that person is doing, then you can say 他在看電腦 or 他在看手機. Note the uncertainty is here partly because both "read" and "watch" can be expressed with the same word 看 in Chinese.
To summarize, if the person is reading a book-like object, then you can generalize 他在看书. If s/he is looking at a digital device, then use the name of the device 他在看電腦 or 他在看手機 UNLESS you know for sure it's an e-book that is being read.