Yes. Most definitely.
There is a good RP community within Eve - the larger part is Amarrian, but there are good groups playing with the different factions as well.
The best introduction is this posting.
Reach out through some of the contacts there.
@Elsebeth_Rhiannon is a good person within the community.
Role playing and PvP are not mutually exclusive - but there are lots of RP players that play a less aggressive game, focusing on industrial activities or exploration, or just generally socially engaging with each other. There are groups across all of New Eden, hi-sec, low and null as well as wormhole dwellers.
There are occasions when groups get into conflict and wars happen. Some of the biggest hi-sec battles are RP related: Thebeka for example. Don’t confuse RP with “soft”. But all styles and engagements are welcome.
And (expletive) it: Elsebeth’s post has just appeared ahead of me…
Well, that’s the Minmatar for you.