Yes, in part, though not quite as such. :)
The -lope part of elope comes from an old verb meaning to run or to go. And the brö- part of bröllop is derived from an older spelling for the modern brud - a direct cognate of the English "bride".
So basically, it's a "bride run", meaning to bring a woman from her old family through the wedding to her new home. And in fact, Old English had a cognate to bröllop as well.