No, we'd need to dissolve that amount into the mix layer (call it the top 50m, for argument's sake), which takes a few months to equilibriate with the atmospher

No, we'd need to dissolve that amount into the mix layer (call it the top 50m, for argument's sake), which takes a few months to equilibriate with the atmosphere through that carbonate chemistry. But, if one managed to do it all at once (not sure how), it would only take a few months. One would want to avoid downwelling regions that get sucked into deep ocean circulation before reaching equilibrium (e.g. the north atlantic), that alkalinity would take a long time to come back up and be useful.