you could jump right in and play some micro ring or cheap buy-in tournies, but because you only need to lose a small amount to have too little to be able to play at all, it probably isnt a good idea.....
$2.00 / .80 min buy-in doesn't allow for much variance and severely limits your play in regards to starting
hands.....with so little margin for error it kinda forces you to play scared, extremely tight....without catching just the right hand it can be hard to make any signifigant gains playng that way.....
and if you do catch that big hand, unless it's the stone cold nuts, all your time spent trying to gain some traction can go right out the window when that 1 outer comes for your opponent
IMO, trying to build on it through more freerolls is a better plan....get up to 8 or 10 dollars before playing buy-ins or RM ring ....then you'll have enough to play a few S&Gs and/or several ring game sessions
skip the 5 hr marathon FT freerolls where you need to make a 1 in 100 finish to cash (top 27 of 2700 pays)
instead, play in some of the innumerable private freerolls with smaller fields .... many of them have miniscule prizepools and spread payouts way too far so that even a near final table finish you're likely playing for just .15 or .25 cents ...but they add up.....could easily triple your br in just a handful of sessions
I'd definitely try to boost the br a bit before risking any of it, but if you do decide to put the $2 in play right away, dont play any large field MTTs...just too many landmines to avoid....better off playing a S&G or a small field private tourny