Well, that's not taking rakeback into consideration. If you can seriously grind out 100k+ hands a month and be a winner doing so, you will be able to hit SNE at some point along the way at which point a winrate of 5bb/100 would actually give you over $2k a month, rakeback included.
However, I don't really think you are aware of what it takes to play 8 hours a day, 5 days a week, every... single... week... and to hit 100k+ hands a month every month of the year.... for only $2k a month.
If the $2k is basically all going to be withdrawn every month for expenses, you will never be building on your bankroll and therefore never be able to move up in stakes. If you can scrimp and live off of $1k or $1.5k a month, then put whatever extra you have back into your bankroll then it will allow you to move up in stakes and make the task that much easier (provided you are still able to win).
Is it possible? Yeah, maybe. Will it be more fun than working a regular job that pays more with less stress and fatigue, gives you benefits, vacation days, and is not subject to leaving you short on rent when you encounter a vicious downswing? Probably not.
Personally, I'm with WV here and that you should probably work for a year or two, play in your spare time, save some money, and if you find you are able to win at 100nl or higher or find you can 24-table and win consistently at lower stakes and you are still serious about making a living from poker to make it happen then.