It's not the parents' consent, it's her guardian's (wali's) consent that matters, which will ordinarily be her father. Two points:
- It depends on whether or not she's been previously married, and
- there's a difference of opinion.
Ordinarily, for previously unmarried women, scholars say the marriage is invalid. There's two sahih ahadith which are clear about this:
There is no marriage without the permission of a guardian. -- Sunan Abi Dawud 2085
Any woman whose marriage is not arranged by her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid. -- Sunan Ibn Majah
However, there's exceptions, e.g. for previously married women (Sahih Muslim 1421).
The Hanafi school of thought is known for being an exception to the rule of marriage requiring a guardian's consent. However, this is not under normal circumstances, as a Darul Iftaa (Mufti Muhammad ibn Adam) explains:
... The relied upon position within the School is that the marriage of a free, sane and adult woman without the approval of her guardian (wali) is valid if the person she is marrying is a “legal” and suitable match (kuf’) to her. ...
... Many Hanafi jurists (fuqaha) have pointed out that it is generally blameworthy and going against the Sunnah to marry without the consent of the Wali regardless of whether the spouse is a legal match or otherwise due to the many Hadiths ...
As such, this Hanafi position is merely a concession (rukhsa) which may be resorted to in situations of need, and a blessing for those sisters who fall victim to their parent’s mistreatment and abuse. ...