PZ Meyers doesn't think so. In taking apart a creationist (a worthwhile thing to do), he's made the following claim:

I actually have some background as a software developer — I wrote some lab automation and image processing software that was marketed by Axon Instruments for several years — and I can tell you as someone with feet in both worlds that the genome is nothing like a program. The hard work of cellular activity is done via the chemistry of molecular interactions in the cytoplasm, and the genome is more like a crudely organized archive of components. It's probably (analogies are always dangerous) better to think of gene products as like small autonomous agents that carry out bits of chemistry in the economy of the cell. There is no central authority, no guiding plan. Order emerges in the interactions of these agents, not by an encoded program within the strands of DNA.

(emphasis mine)

I posted a couple of comments there showing that Richard Dawkins, as an example of someone who is a biologist and not a computer scientist, equates DNA with computer code, literally. From Chapter 5 of The Blind Watchmaker:

It is raining DNA outside. On the bank of the Oxford canal at the bottom of my garden is a large willow tree, and it is pumping downy seeds into the air. ... The whole performance, cotton wool, catkins, tree and all, is in aid of one thing and one thing only, the spreading of DNA around the countryside. Not just any DNA, but DNA whose coded characters spell out specific instructions for building willow trees that will shed a new generation of downy seeds. Those fluffy specks are, literally, spreading instructions for making themselves. They are there because their ancestors succeeded in doing the same. It is raining instructions out there; it's raining programs; it's raining tree-growing, fluff-spreading, algorithms. That is not a metaphor, it is the plain truth. It couldn't be any plainer if it were raining floppy discs.

I think Meyers is in the minority in his opinion, if the comments are any indication, though it seems to be top-heavy with computer people.

As far as I can tell, his argument for why the genome is not a program is:

1) The whole process is bottom-up (there is no executive control)
2) DNA doesn't do all the work (the bulk of the work is done in the cytoplasm by subcellular entities)
3) Environmental input plays a huge role in determining the final product (this is called epigenesis)

At least I think this is the meat of his argument. As several comments in the thread have pointed out, none of these factors invalidate the premise that DNA works as a program. The simple counterargument is that computer programs can (and in many cases do) operate under all three of the above conditions.