You won't get a shapefile @shortessay - you will get an sf object instead:
> library(tidycensus)
> library(leaflet)
>
> ilPop <- get_acs(geography = "county", variables = "B01003_001", state = "IL", geometry = TRUE)
Getting data from the 2012-2016 5-year ACS
Downloading feature geometry from the Census website. To cache shapefiles for use in future sessions, set `options(tigris_use_cache = TRUE)`.
Using FIPS code '17' for state 'IL'
> class(ilPop)
[1] "sf" "data.frame"
sf objects are a way of representing the data you would store in a shapefile. You can use the sf package to read and write shapefiles, and also manipulate their characteristics. The ilPop$geometry column contains all of the spatial data you need for plotting.
> leaflet(ilPop) %>%
+ addProviderTiles(provider = "CartoDB") %>%
+ addPolygons()
Warning message:
sf layer has inconsistent datum (+proj=longlat +datum=NAD83 +no_defs).
Need '+proj=longlat +datum=WGS84'
It should map even with the "inconsistent datum" since the data are in latitude-longitude (NAD 1983). If they were in a projected coordinate system, they would not map. If you are using RStudio, the map should appear in your Viewer tab.
FWIW, I tried running your get_decennial() call and got an error. Can you be a bit more specific about what does or does not happen when you run your leaflet pipeline?