Generally they should work because .NET is backwards compatible. The thing is that such an old version will not work with any modern browser, it may work perhaps with IE8 or IE7 but their market shares are next to non-existent at the moment.
The error itself means that the Response was changed during an AJAX request, which often happens when a server error is thrown and there is a redirect for that, or a file was sent towards the browser during a partial postback. These are general issues that do not stem from our controls, though, and they should not be the reason: https://www.google.bg/search?q=Sys.WebForms.PageRequestManagerParserErrorException%3A+The+message+received+from+the+server+could+not+be+parsed.
Considering that we do not support this old version or .NET 2.0, my best advise is to look into upgrading to the latest version of our controls as well. Articles like this one (all old controls have them, in the same place in the tree on the left-hand side) can help you migrate from your old versions to the current one. I understand this can be a big endeavor but you will get supported software that works on the current browsers (including mobile ones) and a ton of new features and controls.
Do you need help with upgrading your ASP.NET AJAX, WPF or WinForms projects? Check the Telerik API Analyzer
and share your thoughts.