Yes, that's possible. Depending on what NFC reader you are using, you could use either peer-to-peer mode or inverse reader mode (actually Android HCE mode would also be an option, but you would be limited to only some Android NFC devices and you would need to implement code-parts on both ends). One such reader device is the ACR122U. That's certainly not the best choice when it comes to NFC interface devices for PCs as it has many flaws and there exist several versions with wariyng behavior. Still it is one that's widely used and where several example/libraries exist.
Peer-to-peer mode
Android's peer-to-peer mode capabilities are rather limited (you can only transfer a single NDEF message and you can't circumvent the Beam UI). You could use a library like e.g. nfcpy or ISMB-SNEP to implement the NFC peer-to-peer stack on the PC-side.
Inverse reader mode
In this mode, the Android device would operate in reader/writer mode and the NFC interface device on the PC-side would operate in host card emulation mode. You could use e.g. libnfc to emulate an NFC Forum Type 4 tag with certain NFC interface devices. (See also this post on how to put the ACR122U in HCE mode.)