Maybe others will provide their ideas, but I don't think your server will go "down", I think what can happen is that it might "slow down". However, to some users, a "slow" server can be the same as a "downed" server.
I don't use chat on my Moodle because I am one who believes that "chatting" is not targeted at the learning environment, and there are better tools for "chatting" (i.e., SMS, email, phone, etc.). As the Moodle administrator, I also don't what to stumble upon social discussions.
The probability of more than 25-30 students hitting a "post" button at the same time could be low, unless you have some form of activity where you tell students "make your post exactly at 10:30". In Moodle, I don't think that "features" necessarily slow the system down, it is "clicking" that does. How many concurrent "clicks" might you have at any one point in time.
My advice is to pursue your solution, give it a try, see if it works, and if it works well and is being used except it is slow, and if slow, then figure out how to get a little more money to afford a faster service. You will also be learning if you are enjoying being an administrator, or if you need someone else to have this kind of fun.
By the way, I actually have Moodle 2.7 running on a Godaddy hosted server (<$5/month), and on a Bluehost hosted server. Both of these are my "experimental" Moodles. My production moodle, where I might have less than 100 students working, is a VPS (GoDaddy). There are many good hosting companies, and many bad hosting companies, and also many many opinions. But if one company doesn't work for you, don't hesitate aborting and trying another. Pricing is very competitive.