There is always hope, but I would argue that there is not much hope that the UN Secretary General will be able to accomplish much by going to Syria or Egypt. There are two main reasons for this.
First of all, the conflicts in Syria and Egypt are not ones that can be at all easily resolved. There seems to be little in the way of possible compromise, particularly in Syria. In Syria, the Assad regime has treated its enemies in horribly brutal ways (and the insurgents have committed atrocities as well). It is very hard to imagine them agreeing to share power or to partition the country. The same is true in Egypt. The Muslim Brotherhood would surely have a hard time making peace with a government that has killed hundreds of protestors and prisoners. The government clearly sees the Brotherhood as a major threat to Egypt and seems likely to ban it. It is hard to see where compromise would be possible.
Secondly, even if compromise is possible, it is unlikely that the UN Secretary General would be the one who could bring it about. Secretary Ban is not someone who has any stature in the Arab world. The UN has little to offer Syria or Egypt and no real way to threaten them. Therefore, Ban does not have any leverage to use to try to push the sides in these conflicts in any way they do not already want to go.
For these reasons, it seems very unlikely that anything will come of this trip.