The transponder and its GPS source would be completely separate from SkyView, but SkyView would still get traffic and weather since your external transponder source would wake up the ground stations, as Craig says.
Now, my obviously-biased suggestion would be to update your SkyView ADS-B Out compliance with our SV-XPNDR-261 and our SV-GPS-2020 position source. That gets you a Mode S transponder with 2020-compliant position source, including antenna, for $2790. If you go with the 335, you're looking at $3795 list PLUS the $300-$400 antenna. Street pricing looks like it would get you down to the mid 3k ballpark.