Yes, you can do that. Just inoculate a starter culture with an aliquot of your competent cells. Or, even better, streak out some of your competent cells on an agar plate, and select from that a single colony to inoculate a starter culture.
The Inoue method, CCMB80 and the rubidium chloride methods all work very well. Sometime these methods call for growing cells at colder temps (18-25C) in SOB media. I've have found these to not be as beneficial as some suggest. And I have yet to see confirmed side-by-side data to support it (would love to see it if it exists). Fast growth at 37C in LB or 2xYT media make cells more than suitable for all standard cloning needs. The most critical variables to me are (i) keeping cells ice cold at all times, (ii) harvest early (OD ~0.3...0.4 max), (iii) flash freezing final cells with liquid N2, and (iv) working quickly (whole process from harvesting cells to them being in the freezer should be no more than 2 hours). Personally I am partial to the rubidium chloride method for cloning strains (DH10b, TOP10, DH5alpha, etc).
Electrocompetent cells are simple to make as well. e.g. here if you need ultra competent cells (really only needed for specialty applications...double/triple plasmid transformation...making libraries...etc). To make them, essentially it's just 3 washes with cold 10% glycerol, resuspend in small final volume of 10% glycerol so cells are OD ~ 100. Freeze.
Edited by labtastic, 10 November 2017 - 07:30 PM.