Answer to your question is - Yes, we can drink the Abhisekha water which is also called the "Charanamrit".
There is a chapter in the Narada Purana which describes the Deva Puja Vidhi, Matrika Nysasa Vidhi etc in details.
Quoting from the above page:
Deva Puja vidhi: Maharshi Sanat Kumara then described to Brahmarshi
Narada the procedure of worship. Having set up the Puja Region with a
Trikona / Chatur kona Mandala with ‘jala prokshana’, a devotee would
recite the Mantras....
He would recite: Om Atma tatwaatmaney namah, Om Vidya tatwaatmaney
namah, Shiva tatwa-atmaney namaha; then perform Avaahana (Welcome) of
the ‘Ishta Devata’or the Personalised Deity present in the form of a
‘Pratima’ (Idol) or Shalagrama or Linga with ‘Pushpanjali’(flowers) as
follows:....
Next, the details of the Shodasaupachara Puja is mentioned which includes Abhisekham and finally this:
The Procedure of ‘Visarjana’or ending of Puja is to offer flowers by
reciting the Mamtra: Yacchha yacchha param sthaanam Jagadeesha
Jaganmaya, Yatra Brahmaadayo Deva jaananticha Sadaashivah/ Thereafter,
the devotee would sip the idol’s ‘Charanaamrita’ saying:
Akaalamrutyuharanam SarvavVyaadhi vinaashakam, Sarva paapa kshayakaram
Vishnu paadodakamm Shubham.
EDIT:
In MAtrikA Bheda Tantram, Lord Shiva makes an interesting revelation. He says Shiva Nirmalaya is mokshaprada or giver of liberation. Anyone consuming it will attain moksha. But as a rule a Jiva has to travel through all the 84 lacs of Yonis before getting final liberation. It can not happen anytime before that. That's why Lord Shiva himself preached against the consumption of Shiva nirmalaya in various other Shastras. ( This Tantram says that he preached that in Vedas and Puranas. )
Sri ChandiKA UvAcha :
AgrAhyam Tava NirmAlyamgrAhyam Karanam Vibho |
MrishA VAkyam MahAdeva Katham Vadasi Yogabhrith ||
Meaning
Sri ChandikA Devi said :
[ You yourself have said in other Shastras ] that your nirmalya
should not be consumed. Being Yogi how did you utter a lie?
Sri Shankara Uvacha:
Chaturasitilaksheshu Yonigarthe Tathaiva Hi |
Bhramanam Kuruthe Jeevastato Mokshasya BhAjanam ||
Etanmadhye MahA GyAnam Yafi SyAd Veeravandite |
Tada MokkshamvApnoti Bhramanam Kena VA Bhaveth ||
Ataeva Maheshani Gupta BhAvam MayA Kritam |
Meaning
Lord Shankara said:
Jiva gets fit for liberation only after traveling through all the 84
lacs of yonis. Now if mahagyana is obtained by it sometime before that
then it will be liberated. How will it travel through all the 84 lacs
yonis then? Hey Devi, that's why i have said that for the purpose of
maintaining secrecy.
In a later verse Lord Shiva clarifies that something that is said jokingly is simply a joke and not a lie. And the same is true for something that is said for maintaining secrecy.
GuptaBhAvArtham Yad VAkyam PariHAsArthameva Cha |
Tadarthameva Tad VAkyam Na MithyA Parameswari ||
Meaning
Hey Parameswari, whatever said for maintaining secrecy or jokingly is
exactly that and not a lie.
In any case, Shiva Nirmalaya is granter of liberation irrespective of who is consuming it. See the following verse from the same chapter:
PApayukto Hi ChandAlo NirmAlyam Grihyathe YadA |
Tada MokshamvApnoti Shivarupi Na CAnyathA ||
Meaning
Even if a sinful Chandala partakes my Nirmalaya he will be liberated,
he will be like Shiva, & it will never happen otherwise.
All the verses are from Sri MAtrikA Bheda Tantram's chapter 4 (or Patala 4).
