Will a device capable of receiving a 200 Vrms input signal happily accept a 200 VDC signal?
The first part of your  logic is often correct.  However there are some instances where it is false.  For example, supposing the input is a transformer, then it may be quite happy with 200 V AC input, but would burn out if you apply 200 V DC because its impedance at DC (ie: its resistance) is very low.  This certainly applies to power transformers, for example those in power supplies (PSUs of the non-switching variety).  While there are probably not many devices whose signal input stages are transformers, there certainly are some.

The second part of your logic (" the opposite is NOT true") is sometimes false, sometimes true (ie: your conclusion doesn't follow).  Some devices happy with a 200VDC input may be happy with 200VAC input, some not.