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Suppose I need a sodium bicarbonate solution (for non-food related reasons). Can I get something resembling it by mixing $\ce{NaOH}$ and $\ce{CO2}$ in water?

Of course one should not attempt to make food in a chemistry lab, so lets rule out the food safety requirements for food-grade baking soda.

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This is certainly one method by which sodium bicarbonate can be produced. According to this Wikipedia article:

$\ce{NaHCO3}$ may be obtained by the reaction of carbon dioxide with an aqueous solution of sodium hydroxide. The initial reaction produces sodium carbonate:

$$\ce{CO2 + 2 NaOH → Na2CO3 + H2O}$$

Further addition of carbon dioxide produces sodium bicarbonate, which at sufficiently high concentration will precipitate out of solution:

$$\ce{Na2CO3 + CO2 + H2O → 2 NaHCO3}$$

The net reaction for this two-step process is then simply:

$$\ce{CO2 + NaOH -> NaHCO3}$$

Note that this is not the common method by which sodium bicarbonate is produced commercially, but it is a perfectly valid method of it's synthesis.

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