The 802.11 QoS implementations I'm familiar with all set the 802.11 QoS types (VO, VI, BE, BK) according to the IP TOS/DiffServ bits (all non-IP traffic goes out at the default priority of BE == Best Effort).
So for most QoS-capable 802.11 implementations, your question boils down to, "If I send an ICMP echo request using certain IP TOS/DiffServ bits, can I force the other host to reply using the same IP TOS/DiffServ bits?". The ICMP protocol does not provide a way to force the other end to use the same TOS/DiffServ bits, neither does IP below it. Neither do UDP nor TCP.
In some brief testing, I found that my QoS-capable Wi-Fi AP's IP stack seems to automatically use the same TOS/DiffServ bits on the ICMP echo reply that were used on the request, but other public hosts I pinged did not seem to do this.
So the basic answer is "No, the protocols themselves do not provide a way for you, on the local device, to specify the QoS flags that the remote device should use when replying to you." But if the remote device is under your control, you could consider editing the traffic priority policies on the remote device.