BOSS SY-300 / How can I use the Sonar synths with it?

Sure, you can do that. I assume it has a MIDI out, in which case you just record the MIDI data from it. I'm guessing it's probably a USB MIDI interface, in which case it'll show up as a MIDI source in SONAR.
 
Just don't expect your guitar parts to always translate well to, say, a piano and sound like a piano player played them. But I'm sure that's not what you're after anyway.

No, the SY-300 doesn't convert pitch to MIDI, nor can it send or receive MIDI note data. At least, not according to its MIDI spec sheet and what Boss have said.

I looked into one a while ago hoping it was a cheaper alternative to the Roland synths, which are full of stuff I have no need for, like modelled guitars, fx and amps, while what I want to be able to do is just use a guitar to control the real synths I already have.

I've never worked out why Roland don't offer a basic MIDI interface that matches their guitar pickup, has inputs for more than one control and sustain pedals and simply takes the signal from theor MIDI pickup as input and outputs it as MIDI over USB and 5-pin connectors. I suspect they might sell quite a lot of them if the price was right.

Jam Origin's guitar to MIDI software is worth a look, though it's a bit of a work in progress still the basic functions are pretty good. http://www.jamorigin.com/products/midi-guitar/

bitflipper
However, that still doesn't preclude recording audio and using software to convert it to MIDI. 

...True .. Maybe I will try to get Melodyne involved to convert the wav to midi. Hopefully it will 80%+ accurate. I noticed in the past, I had spent too much time modifying my input(midi data) from my fishman tripleplay..