Yes it is possible. If you dont have a computer, you can always rent for just an hour or 2 and it would cost you only a small amount of money. On my part, i'm glad i have tools to access the internet and can make money out of zero cash.
Actually you don't need to have a computer just to access your Bitcoin accounts, there are some gadgets that you can use where ever you are, like cellphone or tablet, aside from being convenient to use it is also affordable to buy. Getting involved vwitj Bitcoin doesn't required any amount of money as a matter of fact you can join some signature campaign without paying anything. Just follow all the rules and thats it you will get paid for your work.