Can I add Tiller to my own budgeting template on google sheets?

I would really like to use a budgeting template that includes bill due dates and the rollover capabilities. I really liked money from Excell and so wanting something with the same features but using google sheets.
If I used a template that was not created by Tiller could I still add the Tiller add-on for the bank transaction connection?

Yes absolutely, this is the awesome part about tiller is that you can modify it to fit your needs. Being in spreadsheet form, it is very flexible to your individual needs.

You can link the sheet to your own budget and then use the transactions and or balance history as you wish

I would also encourage you to check out the community built solutions as well though as there are some pretty clever uses of the data that tiller is able to provide there.