Yes, Tortise SVN does work with UFT. Check the UFT Product Availibity Matrix(PAM) for the supported versions.
Micro Focus has provide the following documents which I have found helpful with this issue.
1. Title : [How to configure TortoiseSVN?](https://softwaresupport.hpe.com/group/softwaresupport/search-result/-/facetsearch/document/KM02400996)
Document ID : [KM02400996](https://softwaresupport.hpe.com/group/softwaresupport/search-result/-/facetsearch/document/KM02400996)
2. Title : [What are the files and subfolders of a GUI test?](https://softwaresupport.hpe.com/group/softwaresupport/search-result/-/facetsearch/document/KM181680)
Document ID : [KM181680](https://softwaresupport.hpe.com/group/softwaresupport/search-result/-/facetsearch/document/KM181680)
3. Title : [What is the file and folder structure for a Service Test / API script?](https://softwaresupport.hpe.com/group/softwaresupport/search-result/-/facetsearch/document/KM01567860)
Document ID : [KM01567860](https://softwaresupport.hpe.com/group/softwaresupport/search-result/-/facetsearch/document/KM01567860)