They may. I do think a side effect of the Vlad contract is that we have a range now. For example, I don't think Kyle Tucker will top the total of $500m by Vlad for a few reasons; most notably age - Vlad is younger and thus you can extend his contract out longer. Tucker will likely top the AAV of Vlad. So this puts his deal around $3375-$450m IMO. The number the Tucker camp dropped to Lance Brodzkowski is $475m over 10. Expect that to be higher than what they'd sign for - it's a media leaked number. I don' think this is far away from what Tucker would have been expected to sign, say, in December when they traded for him, though, and again, with the Vlad cap, I think we have an idea that these numbers seem...relatively in line and not crazy.
I think it's fair to assume two things about the Cubs as well:
1. They're not run by ignorant idiots. You may not always love every move, but every move remains logical and defensible if you look for it. It means they know the number Tucker would need pre-trade and have discussed that
2. That the Cubs didn't trade 3-years of Parades and Cam Smith just to put out a token offer to appease fans.
I don't know if they'll get the job done, but the difference between $375m and $450m over 12 years is $6.25m. Justin Turner makes $6m in 2025. Again, assuming #1, that the Cubs aren't run by idiots, the difference between the low and the high numbers of that field is a Justin Turner each year - a backup corner expected to get maybe 300 PAs. In 10 years, with inflation, it will likely mean significantly less. It probably means an "in for a penny, in for a pound" situation - there just comes a point when you don't ring your hands over Justin Turners. If we expect the Cubs will earnestly offer the low end, I'm fairly sure that they would offer the high end if #2 remains true.
I can also go through the Hoyer quotes again, but I'll leave that be. Point is...I really think the Cubs will give a good run on Tucker and that the end will probably be Tucker's choice more so than the Cubs refusal.