Yes, though you'll want to update the latest bugfix release for best compatibility. Note that Mono 2.4.2.3 actually includes the real ASP.NET MVC library, which was open-sourced by Microsoft under the MS-PL license.
The relationship between .NET and Mono version numbers is very complicated, as there is no direct mapping between .NET versions and features that Mono has implemented. .NET versions aren't exactly straightforward either, as 3.0 was simply additional assemblies added to the 2.0 framework, and similarly, 3.5 is additions to the 2.0SP1 framework - and the 3.5 assemblies do not depend on the 3.0 ones.
Mono features are driven by demand, using data collected using the Mono Migration Analyser.
For example, Mono has supported core .NET 2.0 features like generics since 2005 or so, but only with Mono 2.0 were the Windows Forms 2.0 and ASP.NET 2.0 components considered feature-complete - except for Web Parts, which will likely never be implemented due to low demand. And there are a couple of very Windows-specific features, like System.Management, which will also likely never be implemented as they simply cannot be mapped to non-Windows systems. Apart from such caveats, 2.0 support is now very complete.
Mono 2.0 also included full C# 3, LINQ-to-objects and LINQ-to-XML support, which are features from the .NET 3.5 framework. With Mono 2.4, the ASP.NET 3.5 features are essentially feature complete, and the only major missing 3.5 feature is LINQ-to-SQL, which should be in Mono 2.6. However, there's still no support for the .NET 3.0 assemblies - WCF, WPF, WF. WCF is being worked on but there are no plans for WPF at this time - some degree of WPF compatibility is provided via Moonlight, the Silverlight implementation.
You can deploy projects using menu option the Build -> Publish. You can publish using http, ftp, or a file share.
This may not be the best option for you depending on your situation. You can always create a custom deployment script to handle any special considerations you have when deploying to your environment.
Best Answer
You need to make sure that when you used the aspnet_compiler command, you specified the virtual directory where the applications would reside with the -v command. For instance, if you want to build and serve a stock ASP.NET MVC application, Mvc1, from localhost/Mvc1, you would need to make sure you use the -v /Mvc1 switch:
aspnet_compiler -f -p c:\projects\Mvc1 -v /Mvc1 c:\test\output
Since this is an ASP.NET MVC application, I would also suggest making sure you explicitly configured Apache mod_mono, rather than depending on AutoHosting. I discussed why in my answer to "Mono 2.4, AutoHosting and MVC".
You can now use the Apache mod_mono configuration tool hosted on the mono website.