Yes, you can, but you may need some kind of "Break out board", or maybe even the arduino. I'm not a hardware guy, but I've looked into it a bit. You can buy a GPS module and antenna for pretty cheap, $25-$50, so I may still tinker with that.

The Viking software will connect to a GPS, but I haven't tried it yet. I will soon, maybe today. I'll let you know how that goes.

Years ago I wrote a bit of Perl code to interface my Garmin with my Mac. It wasn't too difficult to grab the data through the USB port in specified intervals. From there I used a map graphic and overlaid my track on it. I displayed the map with the track in a web browser that refreshed the image every few seconds. Nowadays you can layer images using CSS, so the map and the track could be separate layers and you'd only refresh the track layer using AJAX, so there wouldn't be any flashing on the screen when it updated.

It's possible that the Viking software can do that already. On my app I centered an icon showing your location on the map and moved the map as you moved (like a GPS does). I don't know if the Viking app will do that or not. I suspect not, but I could be wrong.

The Raspberry Pi is the perfect computer for delving into programming. That's exactly what it's made for. I'm thinking about putting together a disk image with Linux and the best of the GPS and Mapping software out there (that will run on the Pi) already installed. That way you can just switch out the SD card when you want to play with your GPS software.

If you get a Raspberry Pi let me know and I'll send you a few disks to play with.