As most have pointed out, as long as you train in the airplane you will fly this is fine. Plus, if you do start to fly an airplane with a GPS get a good check out in that GPS by a CFI who actually knows what they are doing.
More important is the instrument instruction you receive which should spend a good deal of time on the fundamentals of BI before shooting approaches.
Also doing a variety of approaches and not the same approaches over and over. I know some schools specialize in this- they spend 5 days teaching you the three approaches that will be on your check ride. Yeah, you'll pass the check ride... (This is NOT a slam on some of the short courses like PIC which does a very good job).
If approaches are not available some have mentioned simulators which, while not perfect, are great for teaching a light control touch and exposing a pilot to different approaches. Another method is to bring approaches to you. Change the frequency on a chart to a local VOR frequency and shoot the approach (of course do this VFR and make sure you stay clear of airspace conflicts). I've done the VOR/DME TACAN Z 15 @ KMTN in Kentucky, New York, Tennessee and Missouri this way. It's part of my "graduation test" for instrument students.