Heather Corinna replies:
No it is not.
Let's dissect this so that you understand why not.
You don't urinate from within your vagina, but rather from your urethra, a very small, barely visible opening on your vulva between your vaginal opening and your clitoris. To get a better idea of what I'm talking about, have a look at the first illustration here: Pink Parts - Female Sexual Anatomy.
During vaginal intercourse, if a partner ejaculates, that ejaculate is going into or around the vaginal opening, and then the sperm in that semen move up through the vagina into the cervix. Urine doesn't go anywhere near your cerix nor into your vagina, so it can't wash away semen. It also, for the record, can't wash away any viruses, bacteria or parasites when it comes to sexually transmitted infections.
In terms of washing, again, when we wash our genitals, we wash the outside: our mons, outer labia, inner labia, maybe right around our anuses. Even if you try and wash the inside or douche -- which is always a bad idea, and it can cause imbalances in the vagina which can lead to discomfort or infection -- water, soap or a douche solution isn't going into your cervix. Sperm swim fast. Even if you did an Olympic sprint to the bathroom after sex to try and wash out your vagina, you couldn't beat them to the punch.
The opening to the cervix (and you saw where that is if you read the whole of that article I linked you to: it's the neck of your uterus that juts into the very back of the vagina), is incredibly small. Part of why that is is to protect your reproductive organs. If that opening wasn't small, it'd be really easy for us to wind up with cervical or uterine infections that made us infertile and very ill. It's too small for water, but not too small for sperm, which are microscopically teeny-weeny. After ejaculation, they head through the vagina, through the cervix and into the uterus, not inside the vagina, seeking out or trying to fertilize an egg. Urine or water from washing can't get into your uterus.
For more information on how pregnancy happens, check this out: Where DID I Come From? A Refresher Course in Human Reproduction.
If you want to prevent pregnancy and have vaginal intercourse, then you need to use a reliable method of birth control that is highly effective. Condoms are a very easy method for anyone to find, afford and use and when used properly, are very effective. They also protect you from sexually transmitted infections. Other options are female barrier methods -- like a diaphragm, which blocks the entrance to the cervix -- or hormonal methods -- like the birth control pill, which changes your fertility cycle continuously so you don't release eggs to be fertilized, and so it's tougher for sperm to get to the cervix in the first place. You can talk to your doctor or healthcare provider about any of these methods, and figure out which is best for you.
For a basic rundown of various -- real - methods of birth control, have a look right here: Margaret Sanger's Disneyland: Choosing Contraceptives.
And if you or your partner aren't ready to deal with any method of birth control? Then if you don't want to become pregnant, the only right choice is to abstain from sex until you both ARE ready.