If that works out will it work similar to how the normal agent works I mean will we get all the analytics , like how we get for while using the normal .net agent?
Well, not 100% - or I should say: it depends on what you implement. Based on your description I assumed it'd be enough to just implement the event API - like sending transactions, spans, and errors - so you will see all those events. But for example you won't see metrics and of course all the auto instrumentation features will be missing, too. One option you can do here is that you add the agent to the process (not sure this is possible in your case), but you configure it to not capture any transaction - with this the normal agent can collect metrics, and your library can "recreate" transactions, spans and errors from your logs.
Also are there any examples available for use of these intake API's?
I think the docs I linked are the best to look at - when I started working on the .NET Agent I mostly went based on the APM Server docs. Other useful resource is here on the Server repo the spec of the API. You can also look at the .NET Agent source code. In this folder you can find the data transfer objects we send to the APM Server and this class sends the data.