12 V / 140 Ah lead acid battery charging with 24 V / 150 A alternator
Yes you can connect two 12V batteries to a 24V alternator to charge them. You shouldn't. But you can.

First thing: a 12V lead acid battery is not 12V, it's somewhere between around 11V up to around 15V, depending on its state of charge. So if your alternator puts out a static 24V, each battery (if balanced) will see 12V, and therefore will only charge to 12V, which is around 40-60% charged. The way you are supposed to charge batteries is with a constant current, constant voltage source. This works by pushing a constant current into a battery until the battery is around 80% charged. Then it keeps a constant voltage across the battery (usually the fully charged voltage level plus 10% or 20% or so) until the voltage of the battery itself is full.

Balancing: if the two batteries are identical, putting 24V across the pair of them in series would expose them both to 12V. However batteries are never identical. There may be subtle differences in manufacturing, they will have aged differently and a whole plethora of other reasons why they are different. For this reason you should balance the batteries, there are lots of ways of doing this, from basic resistors, or clamping diodes to intelligent active balancing. You don't have to balance the batteries, you'll find many battery powered devices don't use balancing. But it will improve performance and life time of the batteries. This is more important as the power levels being considered is higher.

Charging Limit: batteries have got an advised max charging current. Often this is 1C, or the same current as their current capacity. So for your 140Ah batteries, this would be 140A as maximum charging current. However this varies depending on your battery. Check the datasheet. Personally I wouldn't want to put 150A into a 140Ah battery until I had checked the datasheet, and made sure that the batteries were balanced.

Protection: if you just put them together as you describe you have no over charge protection. You may have some inherent limit in the alternator, as you've quoted it as 24V, if it doesn't charge above 24V you'll be fine. But you should monitor the battery voltage and isolate charging when they are full. This could be done with some circuitry, a micro-controller or simply manually measuring voltage and removing connection when required. Also, adding a fuse is almost always a good idea.

I'm sure there are other points I should have made, no doubt others will comment with those.