I would prefer to execute the healthcheck locally by means of a SQL job and store the results in a table. The next step is to consolidate the data of all servers into a central management server. You have the choice to push it from the local servers to the central server or pull it on the central server from the local servers. You can use linked servers or SSIS to transfer the data.

From the central server you can send an email or use other alerting/information system.

If you search the internet you can find several custom-made/free/payed management scripts available that can give you a good starting point. Just a random example: http://www.sqlservercentral.com/articles/Monitoring/98106/