What goes in MUST come out, and vice versa. So all fans as exhaust will produce significant air flow through the case and remove heat with it. But the question is, how efficiently?
For any one fan, the actual rate of air flow through it (assuming there are no significant objects in the air path to interfere) depends on the DIFFERENCE in pressure between the intake and output sides of the fan. The greater that difference, the LESS air flow is delivered for the same fan speed. If all your fans are exhaust, then each is facing basically just room air pressure at the discharge side. On the intake sides, each is dealing with sucking air from inside the case, and that means sucking it in from the whatever openings are available. The result is that the air pressure inside the case is significantly LESS than room pressure, so the pressure DIFFERENCE each fan is dealing with is higher, reducing air flow. Alternatively, if you arrange some of the fans as intakes so there is a rough balance of air intake and exhaust flows, each fan is dealing with less pressure difference (close to zero if balanced), and thus each can produce higher air flow.
So how do the numbers balance out? Say you have six fans, as an example. If all six are exhaust, total air flow is SIX times the output of ONE fan. If you split them as 3 intake and 3 exhaust, each intake fan's air flow is the SAME as that from an exhaust fan, so total air flow is THREE times one fan's. BUT what does each fan do under those two different scenarios?
Look at the specs for case fans. There are two that are pertinent here : Air Flow and Pressure. Understand what those mean: at max fan speed, if there is NO airflow obstruction or pressure difference to impede the fan, it will deliver that max air flow. As output area pressure increases due to air flow restrictions OR as intake pressure decreases for a similar reason, air flow deceases. At some max resistance pressure (the "Pressure" spec), the actual air flow delivered is reduced to effectively ZERO flow. A graph line of air flow versus pressure is VERY roughly a straight line for many fans. So, consider the two scenarios. IF you split the fan functions and arrange intake to match outflow, the pressure each fan deals with is nearly zero, because the case internal pressure is the same as the outside room pressure. So each fan can produce its max air flow. But if you make them all exhaust fans, the (negative) pressure each is dealing with is certainly more than zero, and its air flow is reduced. IF the pressure is HALF of the max pressure spec for that fan, then its air flow will be reduced roughly to half of its max. And don't forget, CASE ventilation fans are of the "Air Flow" type - that is, they are designed to work very well at very LOW pressures, so even small air flow resistance pressures can reduce their flow delivery a lot.
Those are the trends and considerations. Unfortunately, there are enough unknowns here that, for any particular situation, the only accurate answer is to arrange to do complex measurements beyond the scope of the average home computer builder. Impractical! Personally, I'd opt to do the balance thing.