Just filling the overflow tank and not having any water in the engine block sounds like a bad idea to me. One thing for sure; the temp. gauge sender will not read correctly until the sender is in liquid. Thus, how do you know what the real temperature of the engine is until the coolant is flowing? And, the thought of cold water going into a hot engine block doesn't seem right to me. If you are in a hurry, add coolant in the top radiator hose at least. And I would think that is why the T-stat has that little bleeder on it; so you can do it the "book" method way. Anyway, just some thoughts that may not have been considered.

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Paul 1987 300 SDL; 2000 ML; '69 MGB; '68 VW Fastback