some anarchists absolutely use democracy not just "in their propaganda," but in their analysis of a proper anarchist society. usually direct democracy is their preference - with one vote to each person (and the concomitant assumption that all people know and care equally about all decisions...)
cindy milstein and other bookchinites are quite attached to this analysis, for example.
1. you can bypass (as AF says) hysteria associated with the word anarchy
2. you can ease into more complicated conversations by associating the things that people generally like about the word democracy (whether or not you think they actually go with democracy) with other concepts too
2. is a con, as well. sometimes the jarring of people's assumptions is helpful to have them understand that something new is possible/desirable.
1. monitoring our own language makes us feel less connected or authentic with people
3. attempting to smuggle concepts under the camouflage of accepted words can reinforce the valuation of those words. ie if we're saying democracy is a good thing - just define it in this different way, people are likely to leave the conversation just having heard that democracy is a good thing. so we could actually be strengthening people's bias towards a concept that we disagree with.
post script: any question about what terminology to use easily turns into (or already is) a question about principle vs connection (for lack of a better word). it seems easiest to connect with other people when you use terms they understand and when you seem to agree with them. but it's also true that those connections seems (or can become) the most shallow kind of relationship. but sometimes relationships need a longer curve to intimacy than other times.
i am most prone to stand on principle, and that's not uncommon for certain kinds of anarchists, but it's easy to argue that that is based on a kind of alienation from others that this society promotes, and not particularly healthy.