Can you use a PoE splitter to convert from 24V PoE to 5V DC with Gigabit speeds?

I need to check whether you can use a PoE splitter to convert from 24V PoE to 5V DC at Gigabit speeds.

The type of adapters I found allow you to connect an Ethernet cable from the PoE device to the adapter, and then connect the adapter's power and Ethernet to the non PoE device. However to my knowledge, this can only yield Fast Ethernet speeds. To avoid this, would it be possible to only connect the adapter's power to the non PoE device, and connect a separate Ethernet cable (just for data) between the two devices?

The reason behind my query is that I'm intending to get a Mikrotik Hex PoE RB960PGS Router and power 2 TP-Link EAP225 V3 access points using the 24V Passive POE supplied through the router's stock power supply. (AP's are not compatible with the Mikrotik's 802.3af/at protocols, and hence I must use Passive PoE). I'm also intending to get a switch, however there doesn't seem to be a PoE powered switch that can be powered through Passive PoE, as these are supplied by 802.3af PoE (example). This is why I'm considering the possibility to get a non-PoE powered switch and use a splitter to power it up without the need of an extra power outlet.

Thoughts?