In short, no.
IPUMS’s online data analysis tool is based on public use microdata, which supplies limited geographic information in order to prevent identifiability of respondents. For ACS microdata, the smallest geographic units that the Census identifies are Public Use Microdata Areas (PUMAs), which must contain at least 100,000 residents and therefore often straddle multiple counties, cities or legislative districts, etc. From the PUMA information, IPUMS derives some other geographic codes (city, county, metro area) where possible, but IPUMS does not identify legislative districts. You can find the geographic areas for which IPUMS-USA has codes through the Geographic Variables listing.
American FactFinder, in contrast, provides census summary data, which describes geographic units (rather than individuals and households, as in microdata). IPUMS also provides summary data through its NHGIS website, which does include data for state legislative districts.