>>13496633yes, more deltav for manuvers
however for maximum efficiency feeding each engine from the stage beside it isnt enough. you'd want a bigger turbine on the rocket engines running a pump that pumps each booster's fuel into the next booster all the way up the chain to the main stage so only one stage goes empty each time and you dump it.
imagine 1 payload starship with 20 booster staged for fuel, acceleration would be the same since each stage provides its own thrust as well its basically a long line of starships witht he payload one at the end and each time you drop off one at the other end.
limitation is how much engine performance you want to give away for pumping fuel to the next stage (remember the first stage booster that gets dumped first has to basically fuel all the other booster so they'll be full when that stage is dropped)
probably some of the biggest deltaVs you can get on a chemical rocket
