In many professional organizations, the ideals of leadership are more valued than the ideals of traditional management. While managers want control, leaders get out of the way and empower others to innovate. The best ideas often come from cross-functional, self-organizing teams, where new ideas are embraced and encouraged. Sometimes this self-organization only lasts for a few brief moments, just long enough to help foster a new idea.
Do your job, but don't hesitate to help others
I'm a developer, but if I happen to overhear a conversation about how to sell one of our products, and it's something that interests me, I may jump into the conversation and provide some input. Oftentimes, myself and others have planted seeds that have helped solve problems.
Most of the time I'm not working on anything pressing. It's important work, and I set goals for myself in order to stay on track, but there always seems to be room to help others. If a server goes down -- the equivalent of a fire -- then anyone with technical skills focuses 100% on the issue. Outside of sensitive, mission-critical issues, we're pretty laid back.
The point is this: There shouldn't be any cons to getting involved or taking initiative to help out in other areas at your work, so long as you don't overpromise or take on work you don't have time for. If there are cons in getting involved, then you may want to take a moment to reflect and ask yourself if you're working in an environment that fosters innovation. If getting involved is looked down on, then your options are to either focus only on your work and be okay with that, or find a place where sharing ideas is encouraged. There's no right or wrong answer; it's up to you.
Observe your colleagues, then try an experiment
You can tell what kind of culture you're working in by observing others. Do you see colleagues getting involved in such discussions? Are those discussions productive? If they are, then that's a good sign that your input will be welcomed.
Even then, if no one else is taking initiative, try it yourself. Use the reaction of your manager and other colleague to determine whether or not this is encouraged. You'll really not know unless you try.
As for the pros, I'd like to think most professional organizations want self-starters in their ranks -- people who go out of their way to go the extra mile and solve creative problems. Thus, if you're one of these people, it may help increase your chances of advancing your career while also finding a workplace you enjoy! As one who works in such an environment, I assure you, it's quite rewarding. There are challenges, of course, but there are no cons.
Circling back to my first paragraph, management and leadership aren't the same things. As a new hire, you can show leadership by involving yourself in company issues and by taking initiative by offering new, fresh insight. Start your career off on a strong note and show your employer and colleagues what you have to offer! If they don't want you involved, they'll go to a private office. Many discussions are held in public precisely to foster more involvement; it's why the company I work for redesigned our offices so that we all work in a single, collaborative space.