In short: Yes, filters from the vis are also applied on dashboards, but no, it won't overwrite it but try to apply both criteria at the same time.
When you have a filter pill in a visualization and save it, this filter will be saved along with the visualization. If you embed the visualization on a dashboard, the filter pill will be invisible but active for that single visualization (not for the whole dashboard). If you add filter pills to the dashboard as well, they are merged with the filters of the visualization.
- You create visualization A with a filter
- You create visualization B with a filter
- You add both of them to a dashboard - vis A will only show documents from hostgroup A, vis B will only show documents from hostgroup B
- You add a filter
myOtherField: C to the dashboard - vis A will only show documents from hostgroup A AND myOtherField C, vis B will only show documents from hostgroup B AND myOtherField C
Keep in mind, it will not overwrite an existing filter for a field but just add an additional filter, so if you
5. Add a filter
hostgroup: C to the dashboard - vis A will only show documents which have both hostgroups A and C, vis B will only show documents which have both hostgroups B and C - most likely this won't return any results at all because each document just has a single hostgroup value - but it can be useful for array fields.