AFAIK, probably not. Although it is definitely true that discussions of these theological issues in English sources are influenced by Christian theology. (Translating a given Sanskrit or Tamil technical term as “grace” or “mercy” or “works”, for example, is intended to help explicate its meaning by reference to a similar concept in Christianity.)
Arguments on theological issues similar to these divided various sects in Indian philosophy and religion at least as far back as the late first millennium BCE, when Brahmanists/Hindus and Buddhists and Jains were disputing such arcane points well before Christianity came into existence. Controversies about the attributes of God and souls and salvation and what-not sound very specifically Christian in our Western ears, but they’re definitely not specific to Christian theology.
Sounds pretty darn post-Vedic to me, with the phrasing of the translation of concepts into English (‘works’, ‘salvations’, etc) maybe informed by a Christian-theological-vocabulary base. In terms of ‘salvation’ and such, probably a closer influence would be Mahayana on ideas about bhakti.