Not unless it's also full of nails, old bicycle parts, cannonballs, pieces of chain, manhole covers, etc.
I've never had rotten wood dull any kind of saw. Dirt will dull a chainsaw mostly because of the speed the cutters are moving. This is why a reciprocating saw is the weapon of choice for cutting roots. The slower moving blade doesn't dull nearly as fast (I typically get about a year of use out of a blade before it gets too dull). Of course, the blades are very cheap compared to saw chains, which is another good reason for using the reciprocating saw.
I've cut very rotten wood with both the Silky and Komelon arborist handsaws, without them dulling. Down close to the ground, if the trunk is rotten with open cracks or wounds, the rotting center can collect a lot of dirt that blows in there, so a chainsaw can get dulled pretty quick. Lots of folks will use an old chain near the end of its useful life for cutting these. The cutting goes slower, but it beats dulling a new or freshly sharpened chain. I keep old chains for the 32" and 36" bars around that I sharpen, but don't waste too much time on doing it. I use them for these occasions, or when I think there is metal in the wood.
Metal in the wood, of course, will dull any kind of saw instantly... but again, if you're pretty sure it's there, you can use a reciprocating saw with a general contracting blade (usually marked on package for cutting wood with embedded nails) for this.