Yes, though only for a few minutes, and only if the eclipse is occurring just as the Moon is rising and the Sun is setting, or the Moon is setting and the Sun rising. A total eclipse occurs when the Earth is between the Moon and Sun, which are directly opposite to each other in the sky.
Seeing both the Sun and eclipsed Moon at the same time would appear to be a geometrical impossibility, but because the atmosphere has a lensing effect, it raises the images of both the rising Moon and setting Sun above the horizon for a few minutes.
For the same reason, day and night are not exactly equal at the time of the fall equinox, because the day is artificially lengthened a few minutes at each end by the refractive effect of the atmosphere, for a total of seven minutes. It is not until three or four days later that the day equals the night.
It is easier to see the scallop of a partial eclipse above the horizon at sunrise or sunset than it is to see a total eclipse, because the Sun is so much brighter than the Moon.