If your T told you it is okay I would go for it. It is up to them to decide what they want to go on their vacation. I once told long term T, when she told me to email her if I needed, that she was on vacation and shouldn't be working, that she got to decide how her she spent her vacation. She was choosing to periodically check her email..

Current T knows often just emailing her is a help to me even if she does not respond. So for this vacation she told me to text if I need to but also reminded me she is horrible about checking her phone. I texted her on Christmas morning wishing her a Merry Christmas. The next day she responded.