?Steve,
Maybe you could explain more what you mean by publish. To lots of people, publish might just mean "Make it available on the web". To others it might be a PDF but I doubt that in your case.
To publish on the public internet, you need an application that can connect to Spectrum Spatial which renders the map/layers ... via its API. Obviously we have Spectrum Spatial Analyst but we have partners and others who write their own applications as well.
As William Dean mentioned, you can also expose anything in Spectrum Spatial via WMS (or WMTS) as long as you have a client (web app, Pro, other GIS) that can access it.
One decent trick to putting a map into WMS is to use a Group Layer in MapInfo Pro. You can create a WMS layer out of multiple layers but you have to get the order right and it can be error prone. If you upload a group Layer, then you can add just a single entity into WMS preserving all the ordering. It makes it a bit simpler. A group layer really is just like a map without a initial center and zoom.
To give public access to the WMS you need to have Spectrum server on a public site or use a proxy. We are working on this for the default WMS that comes with Pro which is way out of date. Actually all that is in place but are just working on finalizing the data layers. If anyone has input on content that would be welcomed as well.
Lastly, while quibbling is not the point, I try not to use the name "workspace" with Spectrum Spatial. A MapInfo Pro workspace contains potentially, multiple maps, layouts, browsers, tool window locations and sizes, printer info etc. Spectrum Spatial has maps, layers, tables and data connections all of which can be used separately or together. But it has no workspace.
Even an Analyst map config is not the same as a Pro workspace.