Short answer. Yes. Article 1020 provides that heirs to whom a share accrues succeed to all the rights and obligations the heir who renounced, or could not receive it, would have had. You do not get the extra share free of its burdens; the debts and conditions attached to it come along with it.
What the law says
The heirs to whom the inheritance accrues shall succeed to all the rights and obligations which the heir who renounced or could not receive it would have had.
Civil Code, Article 1020 — Accretion Carries the Burdens Too. Read the full provision →
The share arrives with its obligations attached
Article 1020 answers this directly: The heirs to whom the inheritance accrues shall succeed to all the rights and obligations which the heir who renounced or could not receive it would have had. Accretion lets a vacant share pass to the remaining co-heirs rather than defaulting elsewhere, but the law does not let them cherry-pick only the benefit. Whatever the original heir would have owed, or been bound by, had they actually received that share, now falls on the heir who absorbed it in their place.
Why obligations travel with the accrued share
This rule keeps accretion consistent with how inheritance ordinarily works. An heir who takes a share of the estate takes it together with its proportionate share of the debts, charges, and conditions the estate carries, rather than a clean slice of assets. If accretion let the remaining heirs absorb an extra share while leaving its obligations behind, other heirs or the estate's creditors would end up worse off purely because one co-heir happened to renounce or be disqualified, which is not a fair or intended result.
What kinds of obligations can come along
The obligations that transfer are those tied to the share itself, such as its portion of the estate's debts, or any condition or charge the testator attached specifically to that portion. An heir absorbing a vacant share through accretion should treat the addition the same way they would treat receiving that share directly, weighing what it adds against what it obligates them to pay or perform, rather than assuming it is simply a windfall on top of their original inheritance.
Why this matters before accepting
Because acceptance of an inheritance generally cannot be selective, an heir cannot accept the accrued share for its assets while trying to disclaim the obligations that come with it. If the burdens attached to the renounced or forfeited share are heavy enough to make the whole inheritance, share and accretion together, unattractive, that is something to weigh before accepting, since accretion does not create a separate, optional gift that can be taken apart from the rest.