Being an invisible DBA is the goal for everyone who want's to be pro-active instead of re-active. A pro-active approach also saves time which can be used for the more interesting and advanced stuff (never stop learning!). The risk of being an invisible DBA (or DBA-team) is that managers will think everything is working fine and smoothly by itself. Their next conclusion (especially from the ones who only manage based on spreadsheets) will be the team can be reduced by several FTE.
The action for the DBA or DBA-team is to frequently, clearly and loudly mention each and every improvements, prevented incident, etc. to the management!
** Don't mistake the ‘stupidity of the crowd’ for the ‘wisdom of the group’! **