I don't think the the pulse accumulator works that way. It's there to count external events that happen on the pin as far as I know. I've never actually used it though.
I really wouldn't worry about the overflow interrupt. They only occur once every 65536 timer cycles, and if you scale your timer clock then there could be many CPU cycles for each timer cycle. Even though it still could happen many times a second, it is a relatively rare event from the CPU's prespective.
You can still get accurate timing even if lots of interrupts happen. The timer's interrupt priority is one of the highest and since it latches values using hardware, the time is still recorded accurately even if there is a software lag to acknowledge the interrupt.