Wherther SapphireIMS engine automatically stops polling a dependent or connected devices when parent device is down?

No. The child and parent data collection will happen independently. Only the alarm generation can be controlled by alarm correlation feature.

If two servers SVR1 and SVR2 connected to switch SW1 and if SW1 is down, SVR1 and SVR2 will not be reachable. In this case, monitoring continue to happen for SW1, SVR1 and SVR2 and if individual thresholds are configured for all three, alerts gets generated depending on threshold set for each. However, if you don’t want to get alerts for SVR1 and SVR2 when core switch itself is down, then we have option to configure alarms using alarm correlation engine to suppress alarms generated by SVR1 and SVR2 and get it only for SW1.

Refer Alarm Correlation section in our online help link Thresholds for more details.