Yes and no Pam. It depends on your municipality requirements, on the design of your plumbing and drainage system, on the amount of water your sump pump discharges / how often.
Some jurisdictions do not allow sump pumps to flood their sewer systems with ground water – your basement drain is in most cases connected to the sewer system or an ejector pump. Flooding your sewer system with rain / ground water might result in sewer back-up into your house.
In some cases sewer and rain / drainage systems are connected into one in which case sump pump discharge into the floor drain would be just like using a drainage system. However, just like I mentioned above, this could result in sewer backup – for example, your sewer line might be partially obstructed and not capable of handling more than your bathrooms, kitchen and the laundry.
It is possible that the basement floor drain runs into the sum pump well or into a well that serves the sump pump and the sewer system (sometimes done by a mistake, lack of knowledge, laziness, poor design, etc.). In such case, the water from the sump pump discharge pipe will be just going back into the well or through the ejector pump into the sewer line (I’ve seen sump pump and ejector pump wells plumbed together as well).
Connecting sump pump discharge pipe to the floor drain might cause spillage / overflowing of the drain.
More information would be very helpful