A somewhat provocative answer is that... it all depends on how good you are!
The ancestors of modern climbing shoes were born in the 30s, with the PA shoes of Pierre Allain, who observed that sneaker were more efficient than hard hiking boots when performing technical climbing. The original idea was improved upon in the successive years with the introduction of models such as the EB Super Gratton. The first real "modern" climbing shoe is often considered the Boreal Firé, introduced in 1982.
However, already in the 20s and in the 30s people were performing ascents rated VI grade in the Welzenbach scale, which loosely corresponds to 5c in the French scale and 5.9 in the Yosemite scale. Some examples: the Lettembauer-Solleder route on Civetta (1925), the Comici route on the Cima Grande di Lavaredo (1935) and the Cassin-Ratti route on the Cima Ovest (1935).
Since the PA shoes were introduced in the 30s (see above), I am almost sure that many of these hard ascents were performed using old school hiking boots.
I think pictures like these showcase really well what people were able to achieve with just hiking boots:
Gaston Rébuffat on the Aiguille du Midi. Year: ? (source)
Walter Bonatti. Place: ? (source says K2 but I think it's wrong...) Year: ? (source)
Moreover, many modern hiking boots have a smooth area on the sole close to the tip (sometimes called "climbing zone") in order to improve smearing on rocks.
To sum up, it is certainly possible to do rock climbing with hiking boots. About how hard, it all depends on your skill!