It's possible, but you need a measure that will separate the natural from the designed. The SETI researchers have identified one reasonable measure: the narrowness of the band of an electromagnetic emission. This is predicated on the observation that the signals we use to communicate are far narrower, in frequency space, than any natural emission we know about.
(I guarantee you one thing, though: if and when a narrow electromagnetic emission of extraterrestrial origin is found, scientists will fall all over themselves proposing natural mechanisms for it. These will likely be testable, however.)
The ID proponents have proposed a different measure, relevant to their assertions: complexity. Natural things, they assert, are simple; designed things are complex. It is certainly a testable approach; the problem is that the measure fails miserably on the most cursory inspection. Bricks are obviously designed, but it is the simplicity of the brick that tells you that. Cars are more complex, but they really are simple compared to, say, a cloud, or a coastline. In fact, it's easy to come up with any number of manifestly natural things that are gigantically, stupefyingly, obscenely more complicated than the most sophisticated artifact.
(ID proponents at this point typically howl that the appropriate measure is not complexity, but "specified complexity". But the key to specified complexity is, ironically, that it is never rigorously specified, so it cannot be used as a measure.)
And I think that's a straw man. That's as much of a straw man as reducing SETI to, "Natural things are complex and designed things are simple." and then rattling off some natural things that are simple to prove how silly they are.
It is certainly a testable approach; the problem is that the measure fails miserably on the most cursory inspection. Bricks are obviously designed, but it is the simplicity of the brick that tells you that. Cars are more complex, but they really are simple compared to, say, a cloud, or a coastline. In fact, it's easy to come up with any number of manifestly natural things that are gigantically, stupefyingly, obscenely more complicated than the most sophisticated artifact.
ID is looking for a specific type of complexity just as SETI looks for a specific type of simplicity -- one that seem clearly "not natural". But at their core, it's not complexity or simplicity that they are looking for. It's "not-natural" and thus "created by an intelligence".
Since you seem to accept the basic idea that searching for the created among the natural is possible, let me toss this back at you. If you wanted to look for some evidence of intelligent design in life, what kind of evidence do you think intelligent design might leave that could be identified? What non-obvious things might you look for?