WeatherAds can be used in two distinct ways: activating/ pausing ads based on the weather (with no bid adjustments), or for adjusting bids based on the weather.
The first option will work with all bidding strategies, since it is not using geo bid adjustments, but simply enabling and disabling geo targets based on latest weather data.
However, if you are looking to modify bids based on weather, then we recommend switching to Manual CPC in Google Ads. Most automated bidding strategies such as Target CPA don't allow geo-based bid adjustments (with the exception of Enhanced CPC).
Automated bidding uses it's own algorithms to adjust bids based on various signals, and the algorithm overrides any manual bid adjustments that are set.
Since WeatherAds works through manipulating the geos based on weather, it's likely that any weather based bid adjustments made by WeatherAds will be overridden by the Google's own automated bidding algorithm, rendering them infective.
You can also confirm with Google directly if there are any other automated bidding strategies that allow for manual geo based bid adjustments. These would then be compatible with weather based bidding in WeatherAds.
Further Reading: How To Set Up a Campaign In AdWords for Weather Targeting