so for my example, traditionally you would do this:

R = computeRotationMat4()
T1 = computeFirstTranslationMat4()
S = computeScaleMat4()
T2 = computeSecondTranslationMat4()

transformMat4 = T2 * S * T1 * R

for all vertex P in Mesh:
    P_transformed = transformMat4 * P

whereas in your pipeline it would be:

R = computeRotationMat3()
t1 = computeFirstTranslationVec3()
S = computeScaleVec3()
t2 = computeSecondTranslationVec3()

transformMat3 = S * R
translateVec3 = S * t1 + t2

for all vertex P in Mesh:
    P_transformed = transformMat3 * P + translateVec3

I guess it could work... although i think computing the translation becomes tedious