The wood will work, but now ...
The strength or rigidity of any assembled structure depends on the joi8nery, whether it's a wood truss or a table. Yes, wood is very stong in compression, probably quite good in shear, fair in tension, but it all depends on the method of joining the pieces. Mortise and tenon joints are favored over others because glue alone is not sufficient. Screws into wood will fail when they become loose and forces are applied.
So, use the best method of joinery you can even if it means more hours and hand work and you will have a lasting piece. The long, thin legs are like "levers" when force is applied at the bottom... it won't take much over that length to apply a lot of force at the joint.
M$T joints provide more long grain gluing surface which is always what you want for a strong joint. End grain glue joints are weaker in comparison. M &T joints even assembled without glue are structurally sound of them selves.
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)