Personally, I can see a scenario where the cheapest Mac Pro is cheaper than the most expensive Mac Studio, but when comparing AS tier to AS tier, the Mac Pro will be more expensive.
In the standard configurations? Probably not. If talking about Mac Studio with every kitchen sink BTO option possible thrown at it? That is like predicting the 'sky is blue' tomorrow. That has little to do with standard configuration or entry level product pricing and everything to do with Apple's margin bloating high end BTO options. If trying to let Apple hoover as much money out of your pocket as possible, climb up on every BTO price ladder possible.
Currently a M1 MBA with everything on it.... $1,999 same price as MBP 14" entry model. ( This is a
two year old model priced as high as a recently updated M2 generation 'pro' model. )
M2 MBA with everything on it ... $2,499 so $500 higher.
M2 Mini with 'everything' $1,899 only $100 short of a entry Mac Studio ($1,999). (and way past the M2 Pro variant).
M2 Pro Mini with 'everything' $4,449 way, way , way past an entry Mac Studio. ( Way past Mac Pro 2013 entry prices).
The M1 generation Mac Studio with 'everything' is $7,999. It is
already $2,000 higher than the Mac Pro entry price. Even if Apple bumped up the entry Mac Pro price to $6,999 , the Studio would still have gapped it by $1K. Two systems both with a "Ultra class" package aren't going to be that far apart.
In general, Apple's 'get everything' BTO pricing has nothing to do with anchoring/setting the entry level prices for the next product on the hierarchy. The max BTO options have sky high markups... so they are expensive. Is Apple going to kept that tactical stance? Extremely likely yes.
It is also pretty likely that Apple is not going to put very high minimal SSD capacity on the next Mac Pro. The current one starts off at 512GB. Apple just kneecapped the new M2 Pro MBP 14/16" with bandwidth drops to save on inventory complexity for those systems ( just one NAND chip. ). Wouldn't do that on the Mac Pro? I really don't see why they would change the 'game' for that system. ( both Studio and Mac Pro will likely start at 512GB. ). That lower starting point just makes it all the more easier for a BTO Studio to 'catch' the Mac Pro entry price.
Sometimes there have been corner case exceptions when product differentiate is relatively small and Apple could get away with it. iMac Pro versus mainstream iMac in 2017. Because the Mac Pro was comatose and probably wanted to highly limit fratricide on the exact same screen, in the exact same size enclosure iMac 27" they started the iMac Pro higher on list price. By the end of the iMac Pro service life though the 2020 iMac with everything was higher though ( max T2 SSD and max RAM from Apple). Pragmatically that was a bit of those lower end iMac Pro replacement at that point (without the second fan ).
For the standard configurations, the 'entry' Ultra for the Studio is $3,999. There is just too large of a gap there with the Mac Pro basic infrastructure charges (presuming they keep the case size the same ). Probably no huge price drop with the Mac Pro. ( Some folks have wished on a Mx Max Mac Pro where supposedly the shift to lower SoC would dramatically drop the price of the Mac Pro. Probably not. On the Studio the gap between entry Max and entry Ultra is $1,400 (and $400 RAM). If knocked back $1,800 still would be short if Apple keeps the MP price at $5,999. At $6,599 would be an even bigger gap. If Studio is 'eating up' some of the old "Mac Pro only" space then the 'low volume tax' on Mac Pro is likely to go up; not down.
P.S. the other major problem there with hand waving at those numbers is that the laptop Max doesn't have anywhere near the PCI-e provisioning ability to get a Mac Pro close to what it should be . two x16 PCI-e v4 clusters. So the different chiplet formulation for a "Desktop" Max package won't cost the same amount of money as the laptop one. That extra I/O need to be a Mac Pro is likely going to get added to the SoC pricing. If Apple is charging $100's for couple more GPU/CPU cores they are likely going to charge $100's more for more high speed I/O also. )