It's annoyingly unclear how far it's a coincidence, but at any rate it isn't completely a coincidence.

As you can see in e.g. the Wikipedia article about the metre, a unit almost equal to the metre but derived from a pendulum was first proposed in 1670 and the idea was in the air when revolutionary France decided to make a new set of units.

This pendulum-derived unit, if adopted, would have made $g$ equal to $\pi^2\, \mathrm{m}/\mathrm{s}^2$ by definition. The proof of this is very easy, and can be found in other answers here, so I shan't repeat it.

(So if that definition had been adopted, the answer to the question here would be an unequivocal yes.)

Here is a link to an English translation of the report of the commission appointed by the French Academy of Sciences. They explain that the pendulum-based definition is very nice but has the drawback that it depends on the second which is a rather arbitrary unit. So instead they propose to take $10^{-7}$ of a quarter of a meridian of the earth.

Now, this unit they've adopted is (1) almost exactly equal to the pendulum-based unit, but also (2) derived in a conspicuously simple way from the dimensions of our planet. So it's overdetermined. Did Borda, Lagrange, Laplace, Mongé and Condorcet (an impressive list of names indeed, by the way!) choose the particular earth-based definition they did because of its closeness to the pendulum-based definition, or not? That's what's annoyingly unclear.

I find two useful clues in their report. They point in opposite directions.

First, they say

in adopting the unit of measure which we have proposed, a general system may be formed, in which all the divisions may follow the arithmetical Scale, and no part of it embarras our habitual usages: we shall only say at present that this ten millionth part of a quadrant of the meridian which will constitute our common unit of measure will not differ from the simple pendulum but about a hundred and forty fifth part; and that thus the one and the other unit leads to systems of measure absolutely similar in their consequences.

which makes it plain that they knew how close the two were, and were glad to take advantage of it. But, second, they say

We might, indeed, avoid this latter inconvenience by taking for unit the hypothetical pendulum which should make but a single vibration in a day, a length which divided into ten thousand millions of parts would give an unit for common measure, of about twenty seven inches; and this unit would correspond with a pendulum which should make one hundred thousand vibrations in a day: but still the inconvenience would remain of admitting a heterogeneous element, and of employing time to determine an unit of length, or which is the same in this case, the intensity of the force of gravity at the surface of the earth.

so they were clearly prepared to countenance the possibility of a somewhat different unit, and the argument they give against this one has nothing to do with its disagreement with the pendulum-based unit that's so close to the metre.

(Though ... if they had ended up plumping for that definition, they might also have proposed redefining the second to be $10^{-5}$ days, in which case they would again have made $g=\pi^2$ by definition.)

I think the first of those passages is enough to make it clear that it isn't a total coincidence that $g\simeq\pi^2$. Borda et al knew that their definition was close to the pendulum-based one, and offered that fact as a (minor) reason for accepting it. But I think the second is enough to suggest that it could easily have been otherwise: my feeling is that if the definition based on meridian length had been, say, 5% different from the pendulum-based one, they would still have preferred it.