Originally Posted by
Brian Holcombe
If I understand correctly what you are describing, the connection between table top and dovetail is either side grain or end grain and in the case of dovetails neither offers strength of any significance.
Running a groove down the batten is not necessarily weak but certainly weaker than the opposite, as a bending motion on the leg acts to split or separate the batten groove.
Grooving a table, less than 1/3 the thickness does not weaken the table in a meaningful way, instead is reduces the table top's ability to warp by breaking up the continuous grain.
Mind you, if I were concerned about putting the batten anywhere I could just use screws.