is it possible to make a logic OR gate with 2 diodes in series like this:
For my project this would be easier to wire than the usual parallel configuration.
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No, not as you show.
Even without getting into the logic, clearly this can't be a OR gate. OR gates have two inputs and one output. No inputs are shown at all, and we can at best guess that the LED is intended to be the output.
Getting into the circuit, note that D2 always has a fixed 1.7 V across it. It won't live long that way. Also, whatever the branch of the circuit with the 5 V supply is doing is irrelevant. The top of D3 will always be at 3.3 V by definition of what V2 does.
All this circuit does is unconditionally light a LED and blow up a diode.
Here is the basic idea for a diode-based OR gate:
It can get more complicated from here, and using transistors for some gain is useful, but nonetheless, this is the basic concept.