Immediate logic says no, the reason for not drinking unattended water is because a snake might have got to it and it is now venomous, which would not be an issue for netila (or would it, any toxicologists here?).
Yet there are deeper reasons to everything and perhaps one of the deeper reasons is a cause to avoid using unattended water for netila.
כתב הרמב"ם ז"ל אם נתגלו גילוי האוסר אותם וכו' בפ"ז מהל' ברכות ונראה שטעמו מדאמרינן בפ"ב דע"ז (ל.) דמים שנתגלו לא ירחץ בהם פניו ידיו ורגליו ולפ"ז יפה כתב רבינו ואפשר דהאידנא שאין חוששין לגילוי כשרים אף לנט"י כלומר דלא תימא אע"ג דאין חוששין לגילוי ומותרים בשתיה מ"מ פסולין לנט"י כמו שמצינו במים שעשה בהם מלאכה או שנשתנו מראיתן שאע"פ שמותרים בשתיה פסולים לנט"י דליתא אלא כיון שנתבטל הטעם ה"ל כמו קודם שנתגלו:
The Rambam wrote "If [the water] was uncovered in a [manner] that forbids them [for drinking] then [they are invalid for hand washing]..." in the [sixth] chapter of the Laws of Blessings, and it seems that the reason is as it says in the second chapter of Tractate Avoda Zara (30a) that water which was uncovered should not be used to wash your face, hands or feet, and accordingly [the Tur] wrote correctly that "it is possible that nowadays when we are not careful regarding [drinking] uncovered water they are valid even for hand washing," that is to say, you shouldn't say that even though we aren't careful regarding [drinking] uncovered water and it is allowed to be drunk even so, it is invalid for hand washing as we find regarding water which was used for work or changed appearance, that even though they are allowed to be drunk, they are invalid for washing hands - that is not the case. Rather since the reason [for avoiding drinking uncovered water] is nullified [the water] is as it was before it was uncovered.
The Mishnah [Terumot 8:4] says that three kinds of liquids become forbidden if left uncovered: water, wine, and milk. The stated reason is that a poisonous snake may have left some venom in them. But Jewish law says that, now that poisonous snakes are not found among us, one may drink uncovered beverages. [Shulḥan Arukh, Yoreh Deah 116:1] But the Vilna Gaon refused to accept the change.