The answer is yes, you can connect a PC to the NAS, either by means of a router, switch or even a crossover cable, even if your only connection to the Internet is wireless. 
Hello,  I'd like to ask a rather odd question. Can I use the wireless network adapter already in my system to receive and transmit data, and connect my Synology NAS using the network card already installed? It appear that the internet provider in our building is no longer going to be able to offer ADSL service, instead, is installing fibre optic services in each unit, along with wireless wifi. There is no provision for getting a wired connection to my desktop computer any longer. This does mean that instead of upload speeds of up to 2Gbs and downloads of 25 Gbs, I can now have 25 up and 60 down. Guess that is a bonus.Thank you, and apologies for asking such a question.
XPS 8930, using wireless Wi-Fi as well as network card