It is rather:
$$\ce{2 Al + 6 H2O + 2 OH- -> 2 [Al(OH)4]^- + 3 H2 ^}$$where $\ce{OH-}$ comes either from hydroxide dissociation, either from carbonate hydrolysis.
$$\ce{CO3^2- + H2O <=> HCO3- + OH-}$$
The reaction with carbonate would gradually slow down as the carbonate/bicarbonate buffer will kick in.
Initial $\mathrm{pH}$ is ( see notes below line ):
$$\mathrm{pH_{init}}=14 - 0.5 ( \mathrm{p} K_\mathrm{b2} - \log{ [ \ce{Na2CO3} ]} )\\= 7 + 0.5 ( \mathrm{p} K_\mathrm{a2} + \log{ [ \ce{Na2CO3} ]} ) $$
because $\mathrm{p} K_\mathrm{a2} +
\mathrm{p} K_\mathrm{b2} = \mathrm{p} K_\mathrm{w} = 14 $ ( at $\mathrm{ 25\ ^{°}C}$ )
As $ \mathrm{p} K_\mathrm{a2} = 10.329$:
$$\mathrm{pH_{init}}=12.17 + 0.5 \cdot \log{ [ \ce{Na2CO3} ]} $$
..and when some $\ce{OH-}$ is spent and $\ce{HCO3^-}$ is formed:
$$\mathrm{pH}=10.329 + \log \frac {[ \ce{CO3^2-} ]} {[ \ce{HCO3^-} ]}$$
From Henderson–Hasselbalch equation
$$\ce{pH} = \ce{p}K_\ce{a} + \log \left( \frac{[\ce{A^-}]}{[\ce{HA}]} \right) $$
If there is supposed all $[\ce{H+}]$ comes from acid dissociation and majority of acid is not dissociated, then :
$$\ce{pH} \overset{cca}=
\ce{p}K_\ce{a} - \ce{pH} - \log {[\ce{HA}]_\ce{total}}
$$
$$\ce{pH} \overset{cca}= \frac12 (
\ce{p}K_\ce{a} - \log {[\ce{HA}]_\ce{total}} )$$
Alternatively
$$\ce{pOH} = \ce{p}K_\ce{b} + \log \left( \frac{[\ce{BH+}]}{[\ce{B}]} \right) \\ \overset{cca}=
\ce{p}K_\ce{b} - \ce{pOH} - \log {[\ce{B}]_\ce{total}}
$$
Then
$$\ce{pOH} \overset{cca}= \frac12 (
\ce{p}K_\ce{b} - \log {[\ce{B}]_\ce{total}} )$$
$$14 - \ce{pH} \overset{cca}= \frac12 ( 14 -
\ce{p}K_\ce{a} - \log {[\ce{B}]_\ce{total}} )$$
$$\ce{pH} \overset{cca}= 7 + \frac12 ( \ce{p}K_\ce{a} + \log {[\ce{B}]_\ce{total}} )$$