Is this a normal approach to learning songs? Will I get better at reading by this method? Any tips or advice?
In your guitar playing, did you do any form of reading? For example, there are chord symbols (letters), and in classical guitar there is notation in the treble clef which doesn't look too different from the treble clef in piano music. I.e. do you have any reading background that you could bring into piano? You'll be relating the notes differently physically, because it's a different instrument, but the notes are still the same.
Absolutely not. Stop memorising and concentrate on reading constantly for now. A good way to practise it is by looking at every note on the page as you play it and saying every letter name out loud (from what is on on the page- not by looking at your hand). If you basically stop reading at once, you're not going to develop the reading skill.