Very good question and superb answer. Shree Shreemad Vedanta Desika and Acharyas of Shree Ramanuja Sampradaya has warned all of us against demigods (devas, devatas) worship.
The demigods worship is totally forbidden for Vishnu-Bhaktas.
From - http://www.indiadivine.org/content/topic/1557149-desikan-tirunakshatram-saraswati-puja-vijaya-dasami/
SrI:
SrImathE rAmAnujAya nama:
Dear SrI VaishNavas,
This mail is only for mAlOlan net.
I think before 5 years, an old lady asked a question before swAmi.
Her question was:
"Can we include (devatAntara) Saraswati picture etc in Saraswati pUja and vijaya dasami along with swAmi dESikan TN and worship her ?"
With kOpam, SwAmi replied to her - (I present the outline of the same)
"Do not ask me what else can be worshiped because we have categorically told that only SrIman nArAyaNan (with AachAryas of SrI sampradAyam and bhAgavatas)is to be worshipped by SrI VaishNavas-prapannas.DevatAntara sambandam is to be avoided in all forms.
Rudran has explained Nrusimha anushtub during his sAtvika period. But he is not in always in satvam and he is not in SrI VaishNava form. He also committed bhagavath apachAram like supporting bANAsura and fighting with BhagavAn himself.
He is not to be worshipped by SrI VaishNavas.
SRTS has clearly explained all related aspects here.
Similarly, though Saraswati is told in Vedas, she too is not always in sAtvika and SrIVaishNava form.
She, out of anger, came in the form of river to destroy the bhagavath AarAdhana rUpa aSwamEdha yAgam done by brahmA at SrI HastiSailam (refer mei-virata mAnmiyam, Hastigiri mAhAtmiyam).
BhagavAn in the form of a bridge (Setu) stopped her and protected the yAgam.
All these dEvatAntarams are not to be worshipped by us.
SwAmi dEsika TN, bhagavath AarAdhanam are comparable to pure cow's milk. But if you have Saraswati etc and thus dEvatAntara sambandam then it is like poisioning the pure milk.
Even if there is one drop of poision in a pot full of pure milk, the milk is not fit to be consumed
"swAmi quoted lot of pramANAms and from SRTS in this context.
Also he mentioned "dAkshiNya ramyA" verse from SrI hayagrIva stOtram of swAmi dESika and said that only perumAL is the absolute gnyAna-prada: (he who gives knowledge to all including dEvatAntarams) and therefore only perumAL is to be worshipped.
Then the lady asked again: "Can we have golu during navarAtri and in that can be have dEvatAntarams" swAmi said: " If your family has an ancestral practice to have golu during navarAtri, you can have it but you being a prapanna should not place any dEvatAntara (bommai) in it. Only keep the idols (bommai) of SrIman nArAyaNan, thAyar and bhagavath avatArams like rAman, krishnan etc".
