No, "ill" is an adjective. That's why 'take' is a valid linking verb in this case, but this might be the only common use for it as such.
:up: I have a feeling that the exception may be due to a change over time in the word class of 'ill'. In 'ill-remembered'*, for example, its function is adverbial. And many dialects use 'poorly' instead of 'ill'; even then, 'poorly' has the function of an adjective - a Yorkshireman speaking dialect would say 'Art [tha] poorly?', to mean 'Are you ill?' But the ending suggests there was something adverbial about it once.
*Possibly a little archaic now, but that's the way I am;-). Today an older(?) person may say 'I well remember the time when...', or even - in a more mannered variant - 'Well I recall...'. But - for the opposite case - we'd say 'I remember only vaguely/mistily/imperfectly' (possibly, with a subconscious and even unrecognized hat-tip to St Paul, 'as through a glass, darkly' ;-)). In that case, it was possible until the early twentieth century to say 'I ill remember'. That adverb is recalled in the compound adjective 'ill-remembered'.
b