[c#] Count the items from a IEnumerable<T> without iterating?

Going beyond your immediate question (which has been thoroughly answered in the negative), if you're looking to report progress whilst processing an enumerable, you might want to look at my blog post Reporting Progress During Linq Queries.

It lets you do this:

BackgroundWorker worker = new BackgroundWorker();
worker.WorkerReportsProgress = true;
worker.DoWork += (sender, e) =>
      {
          // pretend we have a collection of 
          // items to process
          var items = 1.To(1000);
          items
              .WithProgressReporting(progress => worker.ReportProgress(progress))
              .ForEach(item => Thread.Sleep(10)); // simulate some real work
      };

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