What is the trend in hydration entropy of alkali metal ions?
Yes, there is. The following is a plot of the hydration enthalpy versus row in the Periodic Table. Data was extracted from the Wikipedia, not the primary source (Ref 1).
Your thinking is right. The hydration entropy is evidently negative due to structuring of water (including loss of rotational degrees of freedom), becoming less negative for the larger ions (smallest loss of entropy for the cesium cation).

References

Burgess, John (1978). Metal Ions in Solution. Chichester: Ellis Horwood. ISBN 978-0-85312-027-8.