Rather than speculating about whether the carb could be damaged from sitting, I would start her up cold to see if she starts and whether the choke/bystarter works, see how well she idles and how she runs once warmed up. If everything checks out, then no need to worry about the carb. If the bike doesn't start, idles rough or runs rough when warmed up, then at a minimum, the carb will need to be thoroughly cleaned.
I bought my 2009 GV last year with 87 original miles on her for $1,500. The bike sat for several years and stalled when I would slow to a stop. It needed to have the carb cleaned. I had to clean the carb at least 3 times before all was good. No problems since.
Personally, I don't think it matters if the bike is fuel injected or carbureted if you plan on hauling her around. I haul both types of bikes on trailers and on my Versahaul and I've never had a problem. The most important thing is to stabilize the gas if you aren't going to use it for more than a few weeks.
I took the liberty of looking up that year GV on KBB and it shows that Dealer Retail is $2,005 and trade-in value is $1,330. IMO, $2,400 is way too much for this bike. I think $1,500-$1,800 is more than fair for this bike provided there's no body damage and all the mechanicals work as they are supposed to.
