I don't know whether or not T-Mobile can/will disable SMS, but I am a TM subscriber. They are pretty strict about security as far as my dealings with them. When you dial customer care from your mobile, you are asked for your number, area code first, and last 4 digits of the primary account holder's SSN. They did not used to ask for that.
When you reach a rep, they ask you to verify name and address and usually (but not always) ask you for your account's password. (I am not making this up; I have always had a password on my T-M account as well, which you can also use on their website).
I'm with Steve; you do not want just anyone to be calling and messing up your accounts! However, I fail to see how you are getting so much SMS spam (spim?). I have only gotten 2 since I have been with VoiceStream, now T-Mobile ... my SIM card is so old, it still says VStream when I turn my phone on.
Maybe you should demand a new number -- the person who had the phone number before you may be the party causing your grief ...
Good luck,
Claire