It looks like modal is the only behavior by design, but there is a work-around:
With the proper ID, this is analogous to hitting the button with your mouse to open the dialog.
I have never used this myself except to confirm it works in v2010, and my instinct says one ought look for a way to confirm or derive the ID number (or perhaps there's a constant one can use) since this is a hard-coded "magic number" that may change from version to version.
In Word 2010, which I have handy, "Find" is ID:=141, "Replace" is ID:=313.
So you can set up a "programmatic" search, and then call use the above CommandBars method to open the dialog. It ought to be populated the way you want it and ought to be non-modal.
.Text = "test find field"
.Replacement.Text = "test replace field"
.Forward = True
.Wrap = wdFindContinue
.Format = False
.MatchCase = False
.MatchWholeWord = False
.MatchWildcards = False
.MatchSoundsLike = False
.MatchAllWordForms = False
Of course, non-modal also means code execution continues immediately.