Firstly, an introduction of the two groups in question:
Blue Suns (Mass Effect)
The Blue Suns are a "private security organization", in reality a mercenary outfit operating in the Skyllian Verge.
They start out and continue as a mercenary group. Their logo is something like:
Blue Sun Corporation (Firefly)
The blue sun corporation in Firefly a large corporate company, selling food and technology. Its logo is seen across the series:
However various operatives are seen in the series that shows the darker side to the company, who seem to be after River (and River seems to even be spooked by their image). They are however not a mercenary group being called out to whoever pays.
As to links between the two, there are a few:
From the Degrees of Whedon tumblr:
- Seth Green voices Jeff “Joker” Moreau in ME3. Seth Green was Oz in Joss Whedon’s Buffy the Vampire Slayer.
Mass Effect 3 has 1 degree of Whedon.
Even more there are other references to Firefly:
Zaeed at one point calls you "big ***damn heroes," which is a less-censored version of one of the most popular quotes from the show.
One of joker's quotes if you just stand around him without talking: "Sometimes I just want to disable the internal compensators and pull a Crazy Ivan"
As well as this I ran both cast lists (combined Mass effect 1,2,3 and Firefly) through some bash script filters and I can't find any duplicates besides Adam Baldwin.
I'd say the link was tenuous at best, no more influence here than you might imagine from anything else that's inspired the show (and there are a lot of shout outs, especially in ME2.)
The one thing I did find that might be a link or inspiration is Black Suns a mercenary group from Star Wars.