Would my wife be divorced by my oath, "By Allah, if you do that, then you are divorced from me," if I did the thing, and would my sexual intercourse with her after that be considered unlawful cohabitation?

Most scholars are of the view that suspending divorce on a condition brings it into effect when the condition is met, regardless of whether the husband intended divorce or merely a threat. This is the adopted fatwa. Some scholars, like Ibn Taymiyyah, are of the view that divorce does not occur if the husband did not intend for it to take place, and he is then required to pay an expiation for breaking an oath (kaffarat yamin). Accordingly, your wife has been divorced from you due to your breaking of your oath. If this pronouncement does not complete three divorces, and you had intercourse with her before the expiration of her waiting period (iddah), then she has returned to your marital bond by virtue of the intercourse.