So which feature can you not implement? The only I can think of which you'd have real problems are anonymous functions/lambdas. Most other features I think you can implement. It won't look the same, but it will serve the same purpose.
Destructors. It is the defining feature of the language; everything else in the language extends their reach. They are the key to full exercise of code paths, and thus reliable code.
A programmer who makes full use of destructors is simply a better programmer than one who doesn't.