That depends on the client.
A tech-savvy client will most often want full disclosure, possibly even micro-manage the process.
If the client has no interest in technology at all and is more or less leaving it all up to you, then they probably do not care. However, in the sales phase, I would definitely mention the very wide adoption of Wordpress, as factors such as wide adoption, continued development and availability of freelancers are relevant non-technical factors.
When in doubt, disclose the details and see how the client reacts. All (smaller) clients are different and part of your role is to establish functioning two-way communication. The smaller the client, the more individual personalities come into play.
In general, I have found that clients do not care to be involved in essentially technical decisions, like which database or programming language to use. However, when the technical decision is actually a business decision, they want to be involved. For example: On the face of it, choosing 'open source' over a proprietary product seems like a technical decision, but can easily be presented as a business decision, as it involves pricing, vendor lock-in and so on.