Not to my knowledge.

There are basically three outlets for British programming in the US:

BBC America, which is a "basic cable" channel, which means that it's not broadcast on the airwaves, but virtually anyone who pays for TV will get it. They don't tend to show the massive soap operas like Emmerdale or Eastenders, though they will show the more regularly produced soap-opera-like series, like, uh, Footballers' Wives and, uh, Monarch of the Glen. They also usually stick with relatively recent stuff. BBC America is apparently related to the actual BBC only in name (which I assume they license), and, as such, they will also show ITV and other non-BBC shows. It's been running for about ten years now.

PBS, the Public Broadcasting System, is a private organization funded by donations and private and government grants. It airs no commercials. (Well, they do often have short pre- and post-show bumps from corporate sponsors of that particular show, if there are any.) PBS has imported British shows for a long time, at least since the early 80s, and probably before, some as part of the networked programming, where it is generally presented as part of an anthology series (like Masterpiece Theater or Mystery!), and some as, for lack of a better word, filler for the local stations. This is probably where most Americans saw Doctor Who. I know when I was growing up, my local station would show four episodes of Tom Baker on Saturday afternoon, two episodes of Peter Davison on Sunday afternoon, and a single episode of Jon Pertwee late weeknights. Okay, I'm getting off track. They would also show a lot of Eastenders. And I'm peripherally familiar with Emmerdale, so they must have shown it some time. But Yorkshire-wise, they definitely showed All Creatures Great and Small (speaking of Peter Davison). My local station still shows a decent amount of old sitcoms. Did they make an endless supply of Are You Being Served?

The third place used to be the basic cable A&E (Arts and Entertainment) channel. When it started, it was kind of an outlet for high-brow entertainment. (It also shared a channel with Nickelodeon, running from like 7pm to 7am.) In recent years, though, it has become an outlet for reality shows, like almost every other basic cable channel with a budget. Now that role has been taken over by a variety of other basic cable channels. My wife is watching Poirot, Sea of Souls, As Time Goes By, etc. on various channels.