With ASM may be it's possible, but the likely hood is that your virgin methanol was only 99% in the first place, so to have recovered methanol with the same purity is unlikely. I've only once checked methanol purity since I started using ASM and that only because I suspected the process I was using introduced water and indeed it did ... it was off scale on my hydrometer!
The acid test will be if it processes OK in the next batch ... my guess is that it will.
You reasoning regarding water and methanol separation is logical, but I'm afraid it doesn't work as easily as that. Water and methanol are miscible and as such are very difficult to separate. Several of us tried at length to do it with a GL, but regardless of how carefully you control the temperature the methanol will never be pure enough to reuse. It is possible but you need several stages of reflux and to be honest just isn't economical at the scale we work at.
Best bet is to dry the oil very well, use ASM sparingly and then recover the methanol before doing any water washing.