A string is a string is a string as far as Apex is concerned. You don't say where the error messages are coming from, so this is more of a generic answer. Problems would only arise if you run into heap space issues when the page's contents are transferred to the controller as error messages are generated in the browser (if that's the source) and stored on the controller side or should you run into memory issues in the user's browser.
The latter isn't especially likely on a modern machine unless the user has a lot of tabs open, but the former would be with Visualforce's view state limitations of 128k, even though the fields aren't being displayed. That's because the values would be held in memory by the controller until processed or cleared. If using transient variables to transmit them to the user's browser from Salesforce, then clearing them in the controller, you'd presumably be fine if you didn't want to keep them.