It would cock up the longshore drift of the south coast in that area. Tho Hengisbury head would be redundant. Probably the low lying areas would flood at high water and the solent would hold sewerage as it wouldn't "drain" away on the tides. In short you wouldn't win.......why do you ask?
Fresh Water Bay would fill up with gravel within two years, and a new gravel bank about a mile offshore IoW. The current Hurst spit would start extending out to the current gravel bank. Lymington/Keyhaven salt marshes would start restoring themselves. Why do you ask?
From an engineering perspective damming would be unsound. Every effort would be made to minimize the restriction of flow to reduce lateral forces on the new structure.
These days it's unlikely that restriction of flow would meet the strict environmental requirements that would be placed on the project. The Solent being subject to a number of preservation orders to maintain habitat.
I don't know of any modeling research done on this project, I'll check though, but I would suspect that within 10 years of the damming Lymington would be closed and Southampton wouldn't be able to maintain it's 20m operating draught . 50 years on, without major dredging, Southampton wouldn't be able to operate at all. Portsmouth would probably pay for the dam.