We've been having problems with the heat shutting down, and we've checked the filters, etc. He thinks might be a dirty AC coil. It seems strange that this part is not accessible without cutting a hole into the sheet metal of the furnace? Perhas this is just easier than taking all of the ductwork apart? It does seem like I will lose some efficiency somewhere along the line, no matter how well the hole is sealed afterwards? Thanks.

Not all installations have an access panel to that. Mine didn't. Not at first when I bought the house, it does now however. Its not a big thing to cut one and use a sheetmetal cover to cover the hole. It will come in handy for the future.

If you are concerned with efficiency. Just cover those seams with the shiney aluminum tape you can find in a harsware store. Problem solved. Do NOT use DUCK tape... they are NOT the same thing.

And you really don't want to be taking apart ductwork...

#1 that takes a lot of time, and Time = Money. You don't expect him to work for free, do you?

#2 Every time you take ductwork apart, you run the risk its not going to go back to gether exactly right... I.E. its more likely to leak after. They are meant to be put together once. And stay together.

You're tech is correct, Its very common to have a clogged/dirty/obstructed AC coil, regardless whether its always had a filter in plae or not, most filters are 5% efficient and the dust goes through them easily, as the AC coils wet from condensation as is a (cold can of soda) the dust acumulates and builds up on the coils surface upon which the air flow enters the coil.
Generally an "A" coil or upside down V shape, with the air entering the bottom of the A or top of the V, the 1st being commonly found, as a result the A coil cannot be seen except from underseath the furnce, and newer furnaes hve circuitious pathways so you will never get to see that what today, and a hols in the plenum will allow the view from atop or below, but if along side it, forget it, you need to be below it to see the intake side, above always appears clean as that's after the coils wet surfaces have caught the debris. So yes the tyech correct!