the 737NG and 787 can do it all using the APProach mode, older 737 still have to use LNAV/VNAV, and of course if you are equipped to fly other than ILS precision approaches, for example GLS (standard for the last 5 years on our 737s) or MLS, there is no LOC/GS to connect to in the first place. It's called IAN and provides a FMC generated localiser and glide slope alike presentation for NPA approaches.
Whoa. You do LNAV approaches with APP mode in the 737NG?
From my current FCOM:
The approach mode arms AFDS to capture and track localizer and glideslope and can be engaged for dual or single autopilot operation.
One VHF NAV receiver must be tuned to an ILS frequency before approach mode can be engaged. With one VHF NAV receiver tuned, onside AFDS is enabled for guidance and operation.
Do you have a reference?