In literal direct answer to your question – No.
However many modems have many different modes, so to really answer the question, you’d have to read up on the specs for any given brand (or brands).
However – when you mix synchronous and asynchronous in the same sentence, you’re asking for trouble – or at least difficulty.
Look at it from a simple language exchange. If I speak only German to you (and I don’t understand English), and you speak only English to me (and don’t understand German), the chances of our communicating are essentially zero.
The entire reason for protocols goes back to ancient court behavior. A protocol is a pre-defined, pre-agreed-upon standard of behavior. If you don’t perform the right behaviors to convey the message – you’re dead!
In the computer/networking world, protocols can take many forms: Physical (voltage, polarity, wavelength/frequency, syncronization – tied to a master clock), Timing and Ordering. A specific pattern in one place may (or may not) have the same meaning as the same pattern in a different place.
Now that I’ve gotten off my soapbox, let me ask you what I hope is a simple question: What are you actually trying to accomplish? That is – your end objective, not any technical details that might be blocking your way.