In other words, are cognitive resources finite? Let's say, hypothetically, our mind is only processing 2 tasks: word retrieval and executive decision-making. If I have to dedicate cognitive resources to word retrieval, does that necessarily mean it is taking away resources from executive decision-making?
Baddeley's (1992) theory of multiple component working memory may offer a way to think about this. Baddeley, Hitch, & Allen (2009) demonstrated that secondary tasks disrupted executive attention. They presented meaningful 8-word sentences and random word lists to participants and tested the effects of potential attentional disrupters. For example, participants repeatedly spoke a "1-2-3-4" pattern while hearing the sentences and word lists. Participants recalled fewer items correctly in this condition as compared with an earlier baseline measurement.
The results point to limitations on the working memory in terms of the load placed onto the executive control by various subcomponents. It suggests an answer to your question about the finiteness of cognitive resources.
Baddeley, A. (1992). Working memory. Science, 255(5044), 556-559.
Baddeley, A. D., Hitch, G. J., & Allen, R. J. (2009). Working memory and binding in sentence recall. Journal of Memory and Language, 61(3), 438-456.