There is no "if". You
can sing. You, too, can make eminently
funky sounds -
mightay, mightay, 'n lettin' it all hang out, YOW! - if you want to. All you have to do is "make it your own", as
The Police used to say - find your own voice, then
any song is singable if you sing it in your own
voice. You think
Leonard Cohen is a great singer? No, he isn't. But he's got
soul, because he sings his words in his own voice. Same deal with
Johnny Cash.
My singing experience is sporadic, due to B.B. King disease, but I once sang bass in the university chorus, and later subbed in a hardcore band. So I went from singing "Jubilate deo" to singing songs like "Bullshit".
I also was made to sing, on occasion, in bands, when we didn't have enough songs to do. I didn't have a voice back then - it was just an asthmatic approximation of Syd Barrett (though the song itself was an original). People seemed to like it, though.
You just need to find your own voice. For some, it's natural. For most, it's probably not; I myself had to spend years in a zendo, and every koan konundrum brought me closer to finding my voice. Now when I'm singing in the shower, I can do "Remake / Remodel" and sound like me, rather than some fake Bryan Ferry; or "Love and Happiness" and not sound like Al Green. It isn't better than the originals (hell, no!), but at least it's me, it's unique -- it's an apples and oranges thing, rather than "I can't sing like so-and-so, therefore I suck". Now if I could only remember the words to songs.
But the question is "what song...", and I've wasted your time here, haven't I? I envision myself, 10-15 years hence, singing in honky-tonks somewhere, if they still exist. The setlist would include a George Jones song or two, or maybe something from Merle Haggard or Buck Owens. Maybe something from one of Dolly Parton's early LPs. Some of these songs are a bit of a stretch, since I sang bass, remember? Miles Davis used to insist that there was One Right Tempo for a piece of music; the same goes for key - if you try to sing a song in such-and-such a key, just because it was done that way on your favorite CD, you may be in for trouble. Not only do you have to Find Your Own Voice, you have to Pick The Right Key.
But you can do it. You can sing.
I'll start working on "Walk Through This World With Me" the next time I take a shower. My cowboy boots are packed away somewhere, but there's still the need to get the hat. (Note: don't wear these items if you're in the shower). But there's no hurry, I guess, since this is all still ten years away.