If you assume that it's simply linear, then depending on length you could certainly lose if sufficiently incompetent. Of course, then 1D Connect Four would be effectively a tape, and thus a Turing machine capable of encoding 5D Chess... I'll admit the simile doesn't stand much in the way of stress!
I was thinking connect four with only one column. But if you do only 1 row, it is indeed winnable. In fact, in 2D connect four, that is one of my favorite strategies with a new player - try to get two pugs next to each other on the bottom row with space on both sides