It should work, I've used Slingboxes with Genies. The outputs are simultaneous. Using anything other than the component outputs can be challenging as the receiver will ask you to lower to SD output when viewing the guide. Essentially when they went to the HD UI they never implemented an upgrade to the SD version.
Using component with the HDMI connected can trigger a HDCP error. I found adding a basic active HDMI splitter (around $20 on Monoprice) resolves this. The other option is to use component output from the slingbox to the TV and not use HDMI at all (which avoids HDCP). This may not be an issue depending on the handshake your receiver and television make. It may take some trial and error to see if you need the extra step.
I retired my sling box when the Mobile DVR was released this summer. I don't use it much, and Mobile DVR is flakey, but for the occasional use I've been able to get it to work or use the applicable streaming app for that particular channel.