Yes, it is possible to develop relationship without a common language in the commence.
There are some barriers in cases like that, but the people involved in the relation may overcome it.
They may communicate via translator, interpreter, etc. Also, there are other things to aid those interlocutors, such as dictionary and anything about the knowledge of the respective language. It is relevant to consider not only the idiom in a conversation, but also the culture of the other part and the regionalism of the language, avoiding mistakes or missunderstandings.
To be less dependent of things mentioned in previous paragraph becomes the communication more fluid. So, wheter a man or a woman may learn the idiom of each other to have more direct communication by themselves. They can do that when one teaches another or when studying, for example.