This won't really be about Celts, but upon general request I will explain
what do-support means.
There are some constructions (a lot actually) in English that can only be
formed with so-called anomalous verbs (be, have, can, may, shall, will,
dare, must, need, ought, used to and last but not least do): the negative
(e.g. "I won't go there), the interrogative (e.g. Are you coming to my
party?), the interrogative-negative (e.g. Aren't you coming to my party?),
constructions with negative or semi-negative adverbials (e.g. Hardly had we
left when we ran out of petrol), emphatic positive statements (e.g. You
shall (with emphasis) translate Xenophon for me!), so-called PRO-forms in
clausal tags or short responses (e.g. I can't sing, but my brother can. (the
last can) or You haven't seen him, have you (the last have)) and finally
with midposition adverbs (e.g. You can always rely on me).
In nowadays English these constructions need an auxiliary (like be or have
or one of the others above) and when no such auxiliary is around, some form
of "meaningless" do is inserted (e.g. I didn't go there). This is fairly
atypical for a Germanic language (it is also non-existent in romance
languages (as far as I know, and I have a good grasp on French and I know
some Latin, Italian and Spanish to, so its impossible that English inherited
this from French or Latin). In other Germanic languages you just put the
negative next to the main verb (e.g. Dutch: "Ik ga niet" lit. "I go not").
These constructions were possible in some stages of English (e.g. in
Shakespearian English) and lived for a long time next to the forms with
"do-support". Some researcher say that this might be some kind of borrowing
from Celtic languages (e.g. Irish has a construction with some kind of empty
verb in normal positive sentences). I have the articles somewhere and if you
want me to pursue this I can look it up.
(The grammar I used was: De Keyser & all. 1993. Foundations of English
Grammar. Antwerp: Quickprinter. It is the one that is used in the first two
years of Germanic Languages at the University of Antwerp. You should also be
able to find it in Quirk & all. 1972. A Grammar of Contemporary English.
London: Longman. Which you should be able to find in any decent library)
(note: It is not possible to form all the anomalous constructions with every
anomalous verb as some are sometimes used as main verbs (e.g. do: I didn't
do it. the first is anomalous, the second is not.) or are not fully
anomalous (anymore) (e.g. Not much is possible with need anymore and even
that sounds archaic e.g. I needn't say more))
Sorry for the technical and dry explanation, I hope it didn't remind you to
much of your (probably boring) grammar classes, but what did you expect from
a budding linguist.