First off let me start by saying that I'm not providing any legal advice. When in doubt, my mantra would be to follow @GayotFow's advice.
I've done this unknowingly in the past, without any consequence(at least not any that I know of). Based on my reading and understanding of the visa waiver program, this is permissible.
Travel to Ireland using a UK visa
You may be able to visit Ireland without applying for a separate Irish
visa, if you have an eligible UK (short stay) visitor visa and you are
a citizen of an approved country. Read how this works under the Short
Stay Visa Waiver Programme. Travel between Ireland & UK using a single
You can visit Ireland and the United Kingdom using a single visa
issued by either country, if you are a Chinese or Indian citizen. For
instance: You can visit the UK (including Northern Ireland) without
applying for a UK visa, if you have an Irish Visit (Tourist) Visa. You
can visit Ireland without applying for an Irish visa, if you have an
eligible UK (short stay) visitor visa. You can travel an unlimited
number of times between each country with either visa, for as long as
it is valid. Read how this works under the British-Irish Visa Scheme.
You're eligible for both the BIVS and the Short Stay Program.
Here's the excerpt from timatic -
The following are exempt from holding a visa:
Nationals of India with a valid C visa issued by the United Kingdom if
they have first entered the United Kingdom and been granted a stay of
180 days in the United Kingdom. They are visa exempt for a maximum
stay of 90 days in Ireland (Rep.) or until the end of the period of
stay granted in the United Kingdom, whichever is shorter.
Passengers arriving in the United Kingdom, including Northern Ireland,
and traveling to Ireland (Rep.), the visa waiver programme will apply
and only a visa issued by the United Kingdom will be required. The
visit to Ireland (Rep.) must be within the stay granted within the
United Kingdom. Passengers are permitted to travel to a third country
before traveling to Ireland (Rep.) if the visa issued by United
Kingdom is still valid. Furthermore, re-entry into Ireland (Rep.) from
a third country is permitted if the visa issued by the United Kingdom
is still valid and period of the stay granted in the United Kingdom is
still valid. Passengers with a long term visa must visit Ireland
(Rep.) within a period of the current stay granted in the United
Kingdom. Passengers arriving first in Ireland (Rep.) and traveling to
the United Kingdom, including Northern Ireland, and then returning to
Ireland (Rep.) will requre separate visas issued by Ireland (Rep.) and
the United Kingdom. However the visa issued by the United Kingdom will
be accepted under the visa waiver programme for the return journey to