To see if it could be done, I gave Rogue Gold a shot worshipping only TT.
It was extremely difficult, but I managed, barely. I still played Orc. I didn't find any HP-boosting items in shops, and being unable to take even one hit means I had to mostly only fight monsters my own level. (Finding a Balanced Dagger would help a lot.) I also had to use most of the Wall Crunchers to, you know, crunch walls, rather than being able to convert them for more offense. The worst part is that with Binlor, you can ENDISWAL two or three times to be able to tank one hit from a monster and then kill it with first strike. With TT, that's not available.
Anyway, using WEYTWUT plus Tikki's Edge kept my XP problems from being critical. I needed three shots of Reflexes to beat the boss. I got two from killing lower-level monsters and just about lost hope for the third (out of money)--until I realized I could desecrate Binlor's altar. With Pactmaker, of course, I could have taken Consensus instead. (But I don't think any Pact would be worth the piety.)
It occurs to me in retrospect that if I had thought to desecrate Binlor's altar earlier, I could have used CYDSTEPP for several hits against the boss without TT freaking out. With luck, I could even get a natural dodge; alternatively, this could help set up a Quicksilver hit if I ran out of first-strike popcorn.
Dwarf might alleviate the problem of not being able to take a single hit from monsters; on the other hand, I'm not sure, but it might require another shot of Reflexes, which would be tough to find.