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Yes it could have. I've checked in my book and I saw it they were both in the East Coast Grey with Pink line livery and coaching stock in NXEC livery with East Coast branding.
43296 was re-liveried to EC grey and purple in September / October 2011.
Edit - Above taken from Today's Railways UK magazine from the time. I strongly suspect 314 has been done too, I think the HST Group website would tell you.