Is it possible to use the NFC functionality in the nRF52 series chip to read NFC tags?
no the nRF52 is only a TAG so cannot read other TAGs. A reader is required for that.
Little bit more precise answer could be: there is no way how to drive the 13.56 MHz field from nRF52 chip so doing NFC reader does not make sense. On the bright side: there are cheap ICs which will do this job for you so you will only pay by small additional cost + space on PCB and power if you really want this.
Do you have an example of these cheap ICs?
I met NXP, ST Microelectronics and AMS in practice, I know that Infineon and Samsung Semiconductor have them in portfolio as well (no practical experience). If you want something really cheap I suppose EM Microelectronic (Electro Marin) will have something to offer as well. But if you are in this business you already have your sources and if you are not you better find some help or consultancy;)