Yes, this will work with a time range picker. To explicitly add a timerange picker in Simple XML:
<input type="time" token="time_tok" searchWhenChanged="true">
<label>Select time range</label>
<default>
<earliestTime>-7d@h</earliestTime>
<latestTime>now</latestTime>
</default>
</input>
The above input goes into your fieldset tag along with the other information. Note that this example sets the timerange picker to "Last 7 days" as a default, but you can change that, of course.
You can use the resulting time selection in both the populating search and the actual search that creates the report. For example:
<populatingSearch fieldForValue="fieldName" fieldForLabel="fieldName">
<![CDATA[yourDBconnectsearchhere earliest=$time_tok.earliest$ latest=$time_tok.latest$
| fieldsummary maxvals=1 | rename field as fieldName | fields fieldName]>
</populatingSearch>
And
<chart>
<title>Source type count for last 7 days</title>
<searchString>
youractualsearchhere
</searchString>
<earliestTime>$time_tok.earliest$</earliestTime>
<latestTime>$time_tok.latest$</latestTime>
...
</chart>
... View more