Taking into consideration the earlier statement that the Senator is not (or had not the intention to be) an impartial juror, would that Senator commit perjury by swearing the aforementioned oath to "do impartial justice"?
No. One may do impartial justice without being an impartial juror.
And, if so, what would be the potential consequences for that?
None. Unless the other political party gained a super-majority and invoked Article I, Section 5 to expel that Senator, based on their beliefs.
Each House may determine the Rules of its Proceedings, punish its Members for disorderly Behaviour, and, with the Concurrence of two thirds, expel a Member.
For the record,
It would appear that prosecuting a complaint under 18 U.S. Code § 1621 would require the court to review all the statements made by any Senator against whom the complaint is made. Under Article I, Section 6, such statements "for any Speech or Debate in either House, [...] shall not be questioned in any other Place" means the court cannot review those statements.
Therefore, no legal consequences.
18 U.S. Code § 1621.Perjury generally.
(1) having taken an oath before a competent tribunal, officer, or person, in any case in which a law of the United States authorizes an oath to be administered, that he will testify, declare, depose, or certify truly, or that any written testimony, declaration, deposition, or certificate by him subscribed, is true, willfully and contrary to such oath states or subscribes any material matter which he does not believe to be true; or
is guilty of perjury and shall, except as otherwise expressly provided by law, be fined under this title or imprisoned not more than five years, or both. This section is applicable whether the statement or subscription is made within or without the United States.