Sure, I think everyone does.
When I was a teenager, I didn't have really anyone I could confide in or that I was real close with. I recall attending DCs and CAs really hoping that I'd met other teenagers in the area that I could be friends with only to be disappointed as I once again had to watch the "cool" kids make plans without me. Of course, I was a geek and painfully shy and was probably simply overlooked. I know several of those folks today and it wasn't really them, it was me.
When I was a little older, I really wanted a girl. My previous experience taught me that one wasn't going to fall into my lap. Still, it took several years and actually leaving my hometown before I was able to have a clean slate. I worked on reinventing myself since the super geek role wasn't working out too well for me. Of course, I was still a die hard JW and wouldn't dream of dating a "worldly" girl. I actually think being in the working world helped me tremendously grow from a social viewpoint. Lo and behold I found the love of my life and she brought me a sense of fulfillment (and still does). She rounds me out and showed me something that at one point I though was impossible; that I could be loved just for being me.
Later, she spearheaded the efforts to start a family. I was a bit afraid because I was worried that I would fail as a father and let them down. But I took the leap and now realize that I was deprived of something so special that I can't imagine my life now without them. I learned that while there will likely be times that I'll let them down as an imperfect person will do; the only way I could truly let them down is by not showing them every day how much I love them.
Of course, there are times that I thought I'd be fulfilled by reaching certain goals only to be dissatisfied. Those were things like moving up the corporate ladder (there's always a bigger job), moving up the corporate ladder at the KH (ms was only good for a few years then had to be an elder, then had to try and work hard to get on the service committee, be in circuit admin) or even things like graduating college (which I'm glad I did but I needed that just to pull even with everyone I work with). Obviously, discovering that JWs aren't the truth ripped away a sense that I thought was fulfilled that being that I was part of something bigger, doing God's work.
Sorry for the rambling but your question really caused me to reflect on things that are truly important. We're social animals. We need a connection with others to feel complete. You may say God put it there or evolutionary forces pushed human society together but regardless the fact remains that we need unconditional love to feel complete, to feel human.
What you're experiencing is normal. If you believe the Genesis account, even Adam who was perfect couldn't make it by himself. I think maybe your real issue isn't not having a significant other but the dilemma that no longer believing that the WTS is God's spokesman is causing. You don't want to go after a JW because its not fair to her. After all, she'd think she was bagging an super "spiritual man", an elder, but really be getting someone whose heart isn't in it which I'm certain will cause you eventually to "step down" and will lead to potential problems. On the other hand, you realize the issues that dating a "worldly" woman will cause, leading to at a minimum a disgraceful removal from the BOE and possible sanctions if you act like a normal person.
That, my friend, is the source of your issue. You're in no mans land at the moment. In some ways, I envy your situation. Yes, leaving will cause issues with your parents. But you can fade with likely less damage as someone like me. Rebuilding over a religion is simply not something I deem worth doing given the stakes. Maybe that's the case with you as well, I don't know. Either way, until it's resolved, the connection that you want, that you need, will elude you.