Yes. If a supporter is texting to donate from a mobile device using one of the major UK mobile networks (Vodafone, O2, EE or Three), their donation should work.
Please note, however, that some Mobile Virtual Network Operators, such as Asda and Plusnet, do not currently support texts to shortcode numbers such as Donr’s 70085. Attempted texts to short code numbers from a mobile device using a network run by a Mobile Virtual Network Operator may well fail and the donation will not be registered.
Please check with your individual network provider if you have a query about their support of short code phone numbers.