Question: Are there any acrobatic-category aircraft that are also type-certificated/rated and equipped for flight under the instrument flight rules? What limitations would be placed on such an airplane when flying as an IFR aircraft vs. a VFR aircraft?

Answer: 
Yes: Consider the [Zlin Z 242](http://www.zlinaircraft.eu/en/Aircraft/Z-242-L-Guru-en/). The [type certificate](http://rgl.faa.gov/Regulatory_and_Guidance_Library/rgMakeModel.nsf/0/90b7d75a300cdb3d86257829005d4563/$FILE/A76EU%20Rev%205.pdf) shows that it is certified in the Acrobatic, Utility, and Normal categories. In the section for Optional Equipment, the aircraft can be sold with 

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> Communication and navigation equipment VFR DAY, VFR NIGHT OR IFR according to actual requirements of the customers 
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Generally, if the aircraft meets the [minimum equipment requirements](https://aviation.stackexchange.com/questions/1378/what-are-the-faa-requirements-for-an-aircraft-to-be-ifr-certified) and inspections, and the POH, Type Certificate or other manufacturer's documents [allow it](https://aviation.stackexchange.com/questions/9651/can-a-cessna-162-skycatcher-be-flown-ifr-in-imc/9664#9664), an aircraft may be flown IFR in IMC.

There would be no particular limitation on operations specifically because the aircraft is capable of aerobatics, but the pilot would still need to follow their clearance. This would significantly limit the benefit of the instrument certification. (Note that even if deviations in altitude and flight path were approved, aerobatics [still wouldn't really be possible](https://aviation.stackexchange.com/questions/12179/aerobatics-in-firm-imc-how-would-one-do-it).)
Most combat trainers are equipped and rated for IFR. For example, [Pilatus makes the PC-21](http://www.pilatus-aircraft.com/#39)!.