Yes, but that means "that book of his/hers" obviously - not the same thing. In Ulster Irish the form "an leabhar s'agam/agat/aige/aici" etc (often without the article) is quite commonly used instead of the possessive adjective - and not just to differentiate between his/her/their. I don't know if it's used in the other dialects.

Btw I never understood why certain speakers drop the article in "an leabhar s'agamsa" etc. It's a shortened form of "an leabhar seo agamsa" and you don't say "leabhar seo" without the article... So it's weird.
Maybe it's by analogy with "toigh s'againne", itself by analogy with "bhí mé toigh Sheáin" etc (without preposition)...

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Lughaidh, google "Irish Grammar Workshop: an teach s'agam".

Cad é do bharúil?

Chualaidh mé 'n hipitéis sin fosta siocair go rabh 'n múinteoir a luaitear ansin, go rabh sé agam
Níl mé cinnte cé acu "an teach is agam" nó "an teach seo agam" atá ann, ach cha dtabhrann sin an freagar, ní déarfaí "teach is agam" gan an t-alt ach an oiread...

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Bhí mé ag déanamh go mb'fhéidir go mbeadh aithne agat air.

On my side of the Straits of Moyle, there's a fundamental difference between "mo" and "an ... agam". Scottish Gaelic makes a distinction between alienable and inalienable possession -- that's things that can be given/taken away and things that can't.

My mother will always be my mother, so that's inalienable: mo mhàthair.
My book can be sold or given away, so it's alienable: an leabhar agam.

I have seen a longer form of the alienable structure, but I don't know if this is just conservative or has a distinct meaning: an leabhar a th' agam.

Interesting that Irish has lost this distinction.

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A language belongs to its native speakers, and when you speak it, you are a guest in their homes.
If you are not a good guest, you have no right to complain about receiving poor hospitality.

What about 'leabhar agam' vs. 'leabhar liom'?

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

maybe Irish never had this distinction (I don't think it existed in Old Irish), but Scottish Gaelic developped it independently

In Irish you can say (without article so it's indefinite): leabhar agam, leabhar liom, leabhar domh, leabhar do mo chuid, which all mean "a book of mine".

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

As far as I know it's used in the other dialects as well, and sometimes 'instead of the possessive adjective' which is always used to differentiate between similar articles - mo leabhar, do leabhar, etc.

Tá leabhar ansin agus tá leabhar anseo.
But which is mine?
Tá mo leabhar ansin agus tá do leabhar anseo.

Tá a leabhar ansin agus tá a leabhar anseo.
And which is which?
Tá an leabhar seo aige ansin agus tá an leabhar seo aici anseo.

Whether it's as common in the other dialects as in Ulster, I don't know, but there is the famous Munster book "Jimín agus an Baile seo Againne." and there are numerous examples of its use in Ó Dónail.

But I don't know if you have always to use the emphatic form of the pronoun or not.

In Cois Fhairrge dialect, where the possessive pronouns for "his", "her", "your" (pl.), "our", and "their" are all simply pronounced /ə/ (uh), the contrastive form of the nominative pronoun can be added after the noun (see Learning Irish, page 40) to distinguish where necessary:

a chóta seisean "his coat"
a cóta sise "her coat"
ar gcóta muide "our coat"
'ur gcóta sibhse "your coat"
a gcóta siadsan "their coat"

I always found it interesting, even if purely coincidental, that Welsh has the same use of a repeated pronoun after the noun for possessive constructions.

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).