Language contact, especially language shift, is known to accelerate language change. This has commonly been attributed to innovations during the second language acquisition process. At the same time, cultural evolution experiments and models have revealed learnability as a general constraint in language evolution, suggesting that more learnable features (such as morphological simplicity), would be favored by language acquisition in general and not only by second language acquisition. I use multi-agent simulations to test if diffusion of linguistic innovation in language shift may result from a general acquisition effect reinforced by large proportions of learners compared to experienced speakers. Learners introduce a new variant, and experienced speakers accommodate less to learners than vice versa. Results show that this way it is possible to account for a stable low level of use of the new variant with standard population turnover, as well as account for the diffusion of the new variant when the proportion of learners increases due to language shift. With parameters set to demographic data on language shift from Bantu languages to Portuguese in Mozambique, changes in proportions of learners are sufficiently high to account for the spread of new variants but the trajectory of change differs from linguistic data. This qualitative deviation suggests that mechanisms included in recent models for replicator-neutral language change may also be important to account for contact-driven change where some variants are inherently favored.