Does doing pushups increase the weight you can bench press?

[Kwisatz]

I wouldn't be too worried about how much you can bench, since I find that it's not always an accurate indicator of practical strength. For instance, I know lots of people that can bench more than me but I can still dominate them should they choose to arm wrestle me. Alright, so that's a bad example. If I need to lift a television/luggage/computer/case of beverages/person or any combination or multiple thereof I can do a better job and strain less than other people who are supposedly stronger. Of course such things also rely on your legs, back, etc. but I'd still rather be able to do all that then bench a high number.