Yes, this will be a speaker in mono.
You'll need a mixer to mix the left & right signals. You can't "short" the connections together.
If your source is a computer there is probably a mono setting to do it in software.
With line-level signals you can make a simple passive mixer with two resistors, or an active mixer with op-amps, or you can buy a little mixer.
There's no practical way to mix speaker-level signals.
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If I was building an inexpensive speaker, I'd use a coaxial (or triaxial, etc.)
car speaker with a built-in tweeter and some kind of built-crossover. The crossover in these speakers is usually just a capacitor to the tweeter, or with a piezo tweeter they can get-away with no crossover.
And the bigger the better.
6x9's are usually the best way to get a large-inexpensive car speaker. You can find 8-inch car speakers but they tend to be more expensive. (Bigger car woofers are common but 8-inches is usually the maximum for a full-range coax.)
They are usually sold in pairs so you'll get an extra speaker. You can put both in the same box if you want for stereo, or since they are usually 4-Ohms you can wire them in series for 8-Ohms mono.
Note that two speakers in the same box usually raises the tuning frequency (with less volume for each speaker) so it's a trade-off with more cone area.
Have fun!!!