Yes, it's possible to do that. Two options:
#1: Randomize stuff *once* at the beginning of the experiment, store the result in a <list> or <counter>, then use sequential selection from that list / counter for the remainder of the experiment.
#2: Go for random order in the first portion, record the result (again in a list or counter) at runtime, then use sequential selection from said list counter in the 2nd part.
EDITED TO ADD: Example for #2 (#1 would work along similar lines):
<values>
/ itemnumber = 1
</values>
<expt>
/ blocks = [1=block1; 2=block2]
</expt>
<block block1>
/ trials = [1-4=block1_trial]
</block>
<block block2>
/ trials = [1-4=block2_trial]
</block>
<trial block1_trial>
/ ontrialbegin = [values.itemnumber=list.itemlist_block1.nextvalue;
list.itemlist_block2.appenditem(values.itemnumber)]
/ stimulusframes = [1=mytext]
/ validresponse = (57)
</trial>
<trial block2_trial>
/ ontrialbegin = [values.itemnumber=list.itemlist_block2.nextvalue]
/ stimulusframes = [1=mytext]
/ validresponse = (57)
</trial>
<text mytext>
/ items = ("A", "B", "C", "D")
/ select = values.itemnumber
</text>
<list itemlist_block1>
/ items = (1,2,3,4)
/ selectionmode = random</list>
<list itemlist_block2>
/ selectionmode = sequence</list>