In a word? Yes.
In our 50 years of owning cats and 16 years of breeding Ragdolls, we recently experienced our FIRST case of a cat having a reaction to a vaccine. It was an incredibly scary situation, so we felt the need to share and educate our kitty parents.

Signs of a vaccine allergy can happen at any time, even to kitties who have had vaccines in the past and never had a reaction. One of the reasons this can happen is because vaccines are slightly reformulated each year. So your kitty could be fine one year, and then have a reaction to a new vaccine formulation the next year. This also happens with dog vaccines.

Signs of a reaction include but are not limited to:
Vomiting or diarrhea immediately after receiving a vaccine.
Severe itching (Sometimes)
Extreme fatigue (not just a bit groggy)

If your kitten or cat has any adverse reaction within an hour of receiving a vaccine, please bring your kitten to your local emergency vet immediately. They will require treatment (most likely Benadryl and subcutaneous fluids). Also, please call us ASAP with any concerns and to let us know.

Please keep in mind that reactions are a rare occurrence. 
Our goal is to educate.