Dear Raghuram,
Rosaiah can continue as a Chief Minister of ANdhra Pradesh.
Reasons for continuation:
1. He is a member of Legislative Council. (If a person is not a member in both houses appointed as Chief Minister he has to elect any of the house within six months from the date of appointment. ) As he is a MLC no question arised for his disqualification.
2.Congress party has sufficient majority in Assembly, there is no question to face confidence motion.
3.CLP leader can be elected from any of the houses. There is no clause CLP leader to be elected from Legislative Assembly only.
4. MLAs can elect their CLP leader but there is no clause a CLP leader should become C.M.
5.Party can appoint a CLP leader (a CLP leader elected by MLA directed by its party high command) and CM individually .
6.There is saying majority of Congress MLAs signed in favour of Jaganmohan Reddy. Might be signed but its party's high command have to accept.
7.Appointment of Rosaiah as a CM it is Congress party's internal matter.
There is no question arise to Rosaiah constitutionally for continuation as CM.