This is an interesting question, and a different Homeopath may well give you a different answer. If you are undergoing treatment with a Homeopath I recommend touching base with them about acute treatment.
Before we go any further, just to clarify definitions.
Constitutional treatment is looking holistically at everything about a person, and their fundamental underlying normal self, how the dis-ease manifests as well as history.
Chronic treatment refers to something that is long lasting, whether physical or mental/emotional.
Acutes are illnesses or conditions that come on quickly and are short lived.
Subacutes appear to be acute- like headaches- but unlike true acutes they are recurrent and are a manifestation of an underlying chronic condition.
My belief is that you absolutely treat true acutes when undergoing constitutional treatment. If you fall down the stairs then definitely take the Arnica and anything else warranted. This is called using intercurrent remedies. There have been cases when this has stopped the forward progress of constitutional treatment- but usually repeating the constitutional remedy will put you back on track.
Sub acutes are another story. These are either the same dis-ease repeated – a clear indication of an underlying condition- or can be a more difficult to pick series of similar dis-eases. For example, ear infections, coughs, conjunctivitis and colds. They may all look different, just various different acutes. Underlying them is a common thread, a low immunity that needs constitutional treatment- and if constitutional treatment has already been started, it is time to go back for a follow up and further treatment.
Chronic conditions need constitutional treatment- and depending on the length of time, the layers that there are may take one remedy or many remedies over time.
There is no right or wrong time to undergo homeopathic treatment. One reason the consultation takes the length of time it does is to get the full picture of what is happening. Constitutional treatment and acute treatment are not mutually exclusive, and navigating the balance between the two is a partnership between Homeopath and patient. If in doubt, contact your Homeopath to talk through the best way forward.