Not all glues go corrosive with age, but some do, and some can even go conductive as well. I've seen corrosion from glue a number of times, in particular in Nakamichi receivers and CD players.
If I show a photo of corrosion with the glue around the base of a cap, we would always have the uncertainty if some leakage of electrolyte from the cap was involved in causing it. So I show a photo below of assembly glue that was used to hold a larger power transistor (part of a ±18V power supply circuit) to the main PCB in a Nakamichi SR-2A receiver.
This transistor runs quite hot, as one might suspect from the fact that Nakamichi fitted heat spreading wings on it. Even so, the heat from this transistor has toasted/blistered the glue at the leads. You can see a little corrosion on those leads themselves, but also note the corrosion on the jumper in front of the transistor, which is in direct contact with the glue. Also note that all the other jumpers and leads nearby are fine; it is only the one in contact with the glue that has corroded. The heat from the transistor certainly contributed to the degradation of the glue, and it may have enhanced its aging and help lead to the strong corrosion seen here, but I have seen corrosion develop on leads touched by glue where such heat isn't involved.
I think it is important in cases like this to remove the glue from contact with leads, to prevent further corrosion. Its mission (e.g., holding the component in place for wave soldering) has long since been completed. Usually the degraded glue can be pried/scraped off with a small flat-bladed screwdriver or a dental pick as it is quite brittle. Even in the extreme case below, I was able to remove the glue and clean up the board, leaving only a small heat stain on the PCB under the transistor. But the heat over time did degrade the solders on the transistor leads on the underside of the board, and those needed to be reflowed.
