Yes it’s possible. Pretty easy if you’re running My Cloud OS 3. The whole application system uses docker, so you can install any armhf/armv7 docker images.
If you ssh into your device (enable it in your network settings) simply run the command
mkdir /shares/Downloads/.sickrage
docker run -d --name sickrage -v /shares/Downloads/.sickrage:/sickrage -v /shares:/mnt/wd/Public -p 8081:8081 --restart=always madtech/sickrage-armhf
That is assuming you have a share named Downloads.
I personally haven’t run sickrage but I have sonarr running without issue using this method on an EX4100. Bear in mind the ex4 is pretty underpowered to run applications like these, so the interface and post-processing will likely be pretty slow.