Great question, lets start with the 'oversimplification' angle, and then we'll move to the military side of things.

So, yes, it is a little bit too much of a generalisation to say that the Khmer Rouge as a matter of policy would execute those educated in the manner you outline. This is a complex question to answer succinctly here, so for more detail feel free to check this answer about the khmer rouge supposedly killing everyone with glasses.

Yes, being part of the 'intellectual class', would put you at a higher risk of being killed by the state as you would be further away from their version of an ideal revolutionary, but different administrative zones and areas of the country could be better or worse in this regard and there was no central directive from the leadership saying 'kill smart people'. Many who were educated tried to cover this up, likewise those who had ties to the previous regime, and while this kind of background could sometimes lead to being identified as an enemy and killed, it also sometimes proved that you could be useful.

Historian Philip Short in Pol Pot: The History of a Nightmare, outlines the treatment of those individuals who disclosed their biography to the Khmer Rouge in the early stage of the regime:

"Many fell into the trap. But what happened next varied enormously, depending on who they were and, above all, to which part of the country the exodus had brought them. Technicians and skilled workers were sent away in lorries after being promised that their families would be allowed to join them later. When nothing further was heard from them, many deportees concluded that they had been killed. In fact, most were taken to Phnom Penh to help restore production in the factories where they had worked previously. In provincial towns, where the evacuation was on a smaller scale and consequently better managed, factory employees were told at the outset to remain at their places of work."

Chum Mey, survivor of the infamous 'Tuol Sleng Prison', was kept alive because he had experience with machinery and could repair sewing machines.

There is this rather overstated way of speaking about the Khmer Rouge, invoking the phrase 'Year Zero' (one that they never used) and assuming that the movement was about going backward to some kind of farming utopia... that is not completely true. It gets at some of their intentions, but leaves out the fact that they were primarily a marxist-leninist-maoist movement, that moved the populace to the countryside to produce a massive amount of rice that would then fund a proper industrial revolution for Cambodia. This is symbolised in the countries crest, which features a factory square in the middle of irrigated fields. The murderous and callous nature of the regime in discarding those they deemed unable to be part of a society that was built for that aim, should not be understated in that point however.

In relation to their military strength, their drawing heavily from a rural population base did mean that they were generally lacking in sophisticated expertise of some military systems. That is why Chinese officials and advisers were some of the first people to be flown into the country after the Lon Nol regime fell to the communists. These advisers were able to guide the Cambodians when needed, particularly with the use of the military hardware that was being supplied from China.

The biggest deterioration of the Khmer Rouge military did not occur because of a suspicion of intellectuals, but rather a suspicion of Vietnamese subterfuge.

Vast amounts of the military forces that were stationed in the Eastern Zone of the country (the areas bestriding Vietnam) were purged at various points during the regime's time in power. High ranking officials, and their 'strings' of supporters included.

This internal conflict, as well as the sheer loss of quite large numbers of cadre in the 'East Zone Purges', certainly left the military in a less than stable position and to your question 'less ready' when the clashes between Democratic Kampuchea and Vietnam turned into a war and the Vietnamese invaded at the end of 1978. The fact that this invasion lasted about two weeks before reaching Phnom Penh, and the Khmer Rouge abdicating, speaks to this lack of military power that was certainly in some way the result of Khmer Rouge policies... but perhaps not the ones you might assume.