Could any modern launch vehicle have put Ulysses in it's polar heliocentric without going to another planet first?

Barely, but it involving shenanigans even less practical than a Jupiter flyby.

The lowest delta-v cost trajectory without any planetary flybys from Earth to a 1.35AU-5.4AU 79.11° orbit is the following:

1. Do a burn in LEO, reaching a solar system escape trajectory. Cost: 8750m/s
2. At the edge of the solar system, do an inclination change and set the periapsis to 1.35AU. Cost: ~0m/s
3. At 1.35AU, lower the apoapsis to 5.4AU. Cost: 3830m/s

The first burn is quite comparable to what was done for the New Horizons spacecraft. It didn't accelerate quite as much (as it too used a Jupiter flyby), but it was considerably lighter, allowing for an extra mass ratio of 1.3 for the upper stage.

At the moment, we don't have anything much beefier than the Atlas V launching New Horizons, so the extra 3830m/s can't be crammed in anywhere else if we use chemical rocket engines.

But the final apoapsis lowering can conceivably be performed by an ion engine, as 1.35AU is well within where solar panels provide enough power for that. From Dawn acceleration data, this would take two or three passes.

In the end, this ends up taking much more time than doing a flyby of Jupiter.

---

The final orbit of Ulysses is however chosen specifically because it can be achieved with a Jupiter flyby. Aiming for any 79° orbit, we could use the recipe above, just removing step 3)

Doing a heliocentric inclination change of 79° directly from LEO is more in the order of 16km/s, outside our current capabilities.