How can you say it's unlikely without knowing pipe slopes, storm intensity, depth to groundwater, soil type and transmissivity, etc? There are a lot of variables, your Geotech may be able to help come up with a guesstimate on flow rate to expect from the foundation drains. If it's just seasonal high water, then the rising groundwater should drain out gradually via the foundation drain as surrounding groundwater levels rise. If you have proper grading around the structure, and with gutters on the roof properly piped to downspouts/leaders that drain to a storm system or other disposal (so that roof runoff isn't contributing to your groundwater issue) then the foundation drains might function very well draining to a 12" storm drain with adequate slope. I had nearly that exact situation on a project and the foundation drain is functioning quite well draining to a 12" pipe, although we also had the help of a cut-off drain upgradient that intercepts some of the groundwater flow before it ever reaches the foundation drains.
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