Yes, if they are in a WordPress Network (Multisite), and have the same User Name on each site. No, otherwise, though you could find or buy SingleSignOn software that would do that through other means.
Sorry for the delay. I was away and my response to your question got lost.
I took a look, and there are Single Sign-on plugins available, though the ones that looked the most likely to work for multiple WordPress sites that are not part of a WordPress Network, had had very few downloads.
Wikipedia lists some Open Source stand-alone software products.
So, there are definitely some Open Source solutions available. I just don’t have any experience using them.
Thank you very much for your prompt response.
