Group Delay of Mulitrate system
If the group delay values you get are in seconds (rather than samples) then yes, you can essentially add the two group delays.
You can verify this by feeding an impulse padded with zeros into your system. You will get your filter response, which is then decimated and feed into your second stage. The second stage will also then apply it's filter and do it's decimation. Where the peak is in your output response is (relative to where the impulse is) will correspond to the group delay - this is of course assuming your filters have linear phase.
This is essentially determining an impulse response for your overall system, but your system is linear but it is not time invariant i.e. delaying your input by a sample will produce a different output not a delayed one, so it really isn't an &quot;Impulse Response&quot;.