Kevin,
yes you can top up your phone from any computer any where.
I use it to keep my Jamaican sim card active.
BTW. If you have a T Mobile phone with a sim card you can put the Digicel sim in it and it will work. Don't make a regular call with it as you you will roaming and the charges are pretty hefty. However, by dialing *120# it will check your credit for no charge and keep the phone active.