Can random access happen when UE is in DRX sleep mode?

Hey guys, I have a question. In LTE, when UE has no traffic it switches to DRX (discontinuous reception) mode and don't monitor PDCCH (Physical Downlink Control CHannel). There have been many papers discussing it but they all focus on downlink (i.e. eNB transmits data to UE). Since random access is transmitted via PRACH (Physical Random Access CHannel) but there will be some signalling from eNB to UE via PDCCH in random access procedure. So if UE is in DRX sleep mode, a packet arrives in UE's buffer, can UE generate a RA request?

Thanks you guys for answering.