Yes it is possible.
STR = {'a';'b';'c'}; % Use for popup1;
STR2 = {{'f';'g';'h'};{'i';'j';'k'};{'l';'m';'n'}}; % popup2 (after)
Now if the user selects 'a' in popup1, that is 'value' 1, so set the 'string' of popup2 to STR2{{1}}. If the user selects 'b' in popup1, that is 'value' 2, so set the 'string' of popu2 to STR2{{2}}, etc...
If you want the user not to be able to choose a value from popup2 until a choice has been made in popup1, set its 'enable' property to 'off' until the choice has been made. To do this you will have to enable popup2 and fill its string from within the callback to popup1.