Bresenham's line drawing algorithm guarantees
Yes, Bresenham line drawing algorithm guarantees that endpoints are drawn.
The error accumulation is used for drawing and decreased after drawing a pixel, this is the core idea of the algorithm: incremental error is accumulated to avoid division operation, which is costly, but in this context it is something good and it doesn't mean that errors would damage continuity of line or lose endpoints.
The failure of Bresenham algorithm is technically possible only if floating point variable fails to add error, so $$deltaerr := abs(deltay / deltax)$$ is so small that $error := error + deltaerr$ would not increase $error$ at all, but if that happened, image is too big to fit on computer or some kind of clipping algorithm or bigger floating point variables are needed.
It is safe to assume that $\frac{deltay}{deltax} \le \frac{1}{2^{22}}$ is not going to happen.