Not according to p.192.
The Melee Round is broken down into 4 phases, similar to Stormbringer and the like: One is the Statement of Intent; two is Movement of Non-Engaged Characters; three is Resolution of Melee, Missiles, and Spells; and four is Bookkeeping.
Two specifically states:
Thus, some movement can take place during SR, but only for those who start engaged, or that are moving to become engaged.
Now there could have been something on movement in the clarifications thread that I missed, but that's what the book says.
In RQIII (p.48 of the condensed book) there are only three phases to the Melee Round, and all movement takes place during phase two, along with all combat... This is the action phase, and the rulebook states:
And on the same page just below that, in Movement Within the Melee Round
SDLeary