100%. My son goes to a French immersion school in the inner city and it's so busy that they had to take out grade 6 level and move to another school just to keep up with the demand.
As someone who works in the education system, I can guarantee that no new inner city schools are going to be built in the next 25 years. Governments build schools at a glacial pace. Proactively responding to demographic numbers would be shocking. Look at all the suburban schools that are at capacity with a waitlist immediately after opening.
The inner city does have some interesting things going for it school wise. There is a huge rise in alternative programs (french immersion, spanish bilingual, science, arts based, TLC) and these tend to be located in the inner city because of extra space in older schools. The demand for these spaces exceeds capacity. The CBE awards these spaces based students living in the neighborhoods first before opening it up to other neighborhoods. Also, the high school that every student wants to go to is Western (because it is one of the most academic public schools in Alberta). It is extremely difficult to get into Western without an address in its catchment area. Many students I have taught have had parents rent an apartment downtown (they won't move in), just for the address and the ability to get into Western.