Yes it can!
However, the term dimension analysis needs to be seen in its/a context.
Buckinghams Pi-Theorem did not just emerge out of the blue. And, the reason it works is not pure luck. There is a well grounded physical/theoretical basis for it. And it is the basis which allowed for dimesion analysis. Three scientists come to my mind.
Sophus Lie wrote 1888:
Each one-parameter symmetry group allows the reduction of order of the differential.
Buckingham developed his Pi-Theorem in 1914:
Any dimensionally correct relationship involving physical quantities can be expressed in terms of a maximal set of dimensionless combinations of the given quantities.
And finally, Emmy Noether in 1918:
If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.
Of course one could argue, that dimension analysis and the Noether Theorem / Lie Symmetry Groups have different levels of abstraction.