Yes, I do it all the time! I use my dishwasher to clean the
dishes and large pots and pans get washed in the sink at the same
time. All the crud from the pots and pans then gets sent down the
drain through my In-Sink-Erator disposer.
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It would not ruin your in-sink erator. It would not be good for
your drain, but if you only put some wood shavings in the disposal
accidentally once, it would not ruin it.
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There is no H770-sst just the H770-SS which has a SST tank
assembly.