No. Once the solvent has evaporated the glue just melts with the feather.
But if you burn various things using an open flame, ( you can use a cauteriser if you have one of course), then you should not do it where you have been working with glue or similar materials.
Also, when you work with glue and such, do it with plenty of ventilation, or in an open space.
If you burn feathers, they stink, so it it is best to do that in a well ventilated area as well.
Also best to do it where the ash and debris will not fall on your bench or mess anything up.
TL
MC