Yes, classical Arminianism would hold a view similar to what you are describing. But I've met people who don't necessarily agree with Arminianism on everything, yet when they read passages like Ephesians 1 they place the emphasis on the fact that we are predestined "in Christ" - in other words it is Christ as a means of salvation and adoption that was determined by God - not individuals.
Ephesians 1:3-6 -
Praise be to the God and Father of our Lord Jesus Christ, who has
blessed us in the heavenly realms with every spiritual blessing in
Christ. 4 For he chose us in him before the creation of the world to
be holy and blameless in his sight. In love 5 he predestined us for
adoption to sonship through Jesus Christ, in accordance with his
pleasure and will— 6 to the praise of his glorious grace, which he has
freely given us in the One he loves.
God predestines the elect to a glorious future: Predestination is not
the predetermination of who will believe, but rather the
predetermination of the believer's future inheritance. The elect are
therefore predestined to sonship through adoption, glorification, and