Algae is common and is rarely harmful to drifwood nor the aquarium. Thus it is personal preference if you wish to battle it or let it grow...
Algae requires both nutrients and light to thrive. Thus putting efforts towards removing both of these is the best approach.
Fungus isa whole different creature though...
Fungus does not utilize photosynthesis so denying light will not inhibit fungus growth...
There are countless species of fungus that feed off of countless things. While keeping the tank/water generally clean is always best, it will be very difficult to isolate what that particular fungus is using as food. Also it is very possible it is using the wood itself as food in which case it will be weakening the structure fo the wood.
Long story short, I'd try to get rid of the fungus...
As discussed in the other thread, boiling will kill it, but boiling can also soften/weaken droftwood. I no longer advocate boiling driftwood.
Instead I suggest soaking in a warm, strong salt bath. The salt solution should be at least as strong as sea water or a little saltier. Don't worry, you cannot make it to salty. Any salt will work and I would not recommend using aquarium salt simply because there are much cheaper alternatives readily available.
