Oil Pressure Sending Unit - Leak?

Yes they can and do leak. Presumably you have a factory gauge or light and the sending unit looks a little bit like a small can. These can leak from the crimped area, the threads, or sometimes from the top of the unit. When you are installing a new one, make sure you use thread sealer, either Teflon tape or a liquid type of pipe sealant, and don't overtighten it.