Help with Furnace/Central air and Ecobee thermostat

ylomnstr

So I've been using a Lux Geo thermostat for my single zone heat/AC setup. Well apparently the company shut down the servers so I can no longer use their app. So I'm looking at the ecobee essential thermostat now, but I don't have a C wire. I know I can use the ecobee c wire adatper kit, but I'm wondering if it will work with my setup. Currently, my lux geo is using an external USB power supply as that was a main feature as to why I got them. I also have 5 wires connected to the thermostat.

Blue to RC
Red to RH
Green to G
Yellow to Y1
White to W1

When I look at the furnace, the wires are connected as follows:

Yellow and red wire both to Y
Green to G
White to C
Blue to R
The W terminal has no wires.

So my question is, can I use the ecobee with the ecobee adapter? Pics below for reference.