I converted through the conservative movement of my country, would Chabad accept me to watch their services coming from this background?

You must ask them, for Conservative conversions vary totally from place to place, and that's their major problem: that they are not national-minded nor objective, to be accepted by all. Most Conservative rabbis today clearly don't really follow the Jewish law, and accordingly, their conversions are not acceptable. If you wish to be accepted by all, you should do an orthodox conversion. Some Chabad communities, seeing that you are sincere, may accept you in the meantime as someone "in the process". All the best!