Yes,A tie does not necessitate the Vice President to be present in the Senate. Without the VP's vote, the motion will simply fail. However, if the VP wants to break the tie, the VP has to be present on the floor, as the Senate's presiding officer1, if their vote is needed in the event of a tie.
(1more on this in @Damila's answer)
It's worth noting that the Vice President is the President of the Senate which explains their power to break ties.
"The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided" (U.S. Constitution, Article I, section 3).
Whether or not it will make the VP less effective is subjective as that is technically part of the VP's job. The need for the VP to break ties is simply a downside of having a 50–50 Senate majority. Quoting from Axios:
Harris would have to be on constant call for Senate business — but the Democrats would find that preferable to having McConnell and the Republicans control the chamber.
This NPR article provides some insight into how VP Dick Cheney had to be prepared to cast tie-breaking votes in early 2001 when the Senate was tied 50–50.
As a general rule, vice presidents have been pressed into service as tie-breakers when the Senate was controlled by the president's party, especially when the margin of control was narrow. Vice President Al Gore had to break ties on budget votes and other tough calls for the Democrats in the 1990s. Vice President Richard Cheney had to be on call regularly to reinforce Republican control of the Senate early in 2001, when the regular roll call was split 50-50 between the parties. He ultimately cast eight tie-breaking votes.
VP Mike Pence also went to the Senate to cast tie-breaking votes a few times in the early days of his tenure.
Vice President Mike Pence came in to cast tie-breaking votes after the Senate locked 49-49 on both a procedural vote and the confirmation vote on Kansas Gov. (and former Sen.) Sam Brownback's nomination to serve as ambassador-at-large for international religious freedom.
However, a tied Senate does not mean that VP Kamala Harris will always have to be in the Senate. Often, it is clear early on if an impending vote is controversial and requires the VP to break a tie. Hence, the VP would likely be given sufficient advance notice and only need to be present on the Senate floor when that vote is taken.