No. First, every kilogram we send to Mars will be hugely expensive, so low mass will be prioritized over long-term sustainability for research and exploration missions.

Second, the plants chosen for bottle gardens are very sturdy and tolerant of non-optimal environments. Humans are a lot more sensitive.

If you're interested in the topic, read "The Martian" by Any Weird, a very well-researched SF story about an astronaut who gets left behind during a Mars mission and has to survive for several years using equipment that was only specced to sustain the expedition for a month.

It's been proposed countless times, there are numerous challenges to overcome and the benefits are hard to convince people of.

There's also the issue that it will cost tens or hundreds of billions of dollars to put people on another planet for an extended period of time.

Elon Musk wants to put thousands of people on mars [1] and he's one of the very few individuals with the resources to actually do it successfully. He has had some highly ambitious goals in the past (rocket ship company, electric car company) and has been wildly successful.

NASA supposedly had some funds appropriated to them recently for missions such as researching Mars colonization, they have had plans and discussions of what would be necessary for basic Mars colonization for decades. [2]

[1] http://www.wired.com/2012/11/elon-musk-mars-colony/

[2] https://www.google.com/search?q=mars+colonization&tbm=isch

https://www.google.com/search?q=plants+on+mars&tbm=isch

http://nextbigfuture.com/2013/12/elon-musk-provides-more-det...

The only problem is getting it to Mars. Space travel isn't hard or anything, and surviving the rigors of space flight isn't easy.