Chemicals are signals. For example, a hormone is pretty much by definition a signaling chemical.
Plants most definitely have information processing. The entire process of 20th century computation reveals that you can get 'intelligence' from really stupid things (NAND gates) - conversing that we can have computation (and all that implies) from a variety of different substrates (neurons, mechanical relays, semi conductors, quantum bits, etc). People tend to get panicky and start delineating things so that they can restrict plants from 'having thought' but its all pretty silly.
Plants most definitely have information processing. The entire process of 20th century computation reveals that you can get 'intelligence' from really stupid things (NAND gates) - conversing that we can have computation (and all that implies) from a variety of different substrates (neurons, mechanical relays, semi conductors, quantum bits, etc). People tend to get panicky and start delineating things so that they can restrict plants from 'having thought' but its all pretty silly.