Partial answer only.

This could turn out to be quite a complicated question to answer fully, but it turns out that they've done the experiment for the Falcon Heavy and we know the answer for that one at least.

The Tesla Roadster launched first to a high apoapsis (about 7000 km) elliptical LEO orbit and stayed there for 6 hours and then went off to deep space by burning every last bit of propellant.

That resulted in a heliocentric orbit with a perihelion of 0.99 AU and aphelion ~1.7 AU.

It is now catalogued as such.

You can find out where it is now and where it is going and how fast at https://www.whereisroadster.com/

So a "how fast could it go" question really depends on what orbit you put it in. If you aim for a highly elliptical heliocentric orbit then at perihelion (closest to the Sun) it will be going a lot faster than at aphelion one-half period later.

I think that ultimately you question could best be phrased as

What is the air speed velocity of an unladed swallow Falcon?

To which the answer is

African or European?

or even better:

What heliocentric $C_3$ can a Falcon 9 achieve with zero payload?

For more on $C_3$ see https://space.stackexchange.com/search?q=user%3A265+C3

Partial answer only.

This could turn out to be quite a complicated question to answer fully, but it turns out that they've done the experiment for the Falcon Heavy and we know the answer for that one at least.

The Tesla Roadster launched first to a high apoapsis (about 7000 km) elliptical LEO orbit and stayed there for 6 hours and then went off to deep space by burning every last bit of propellant.

That resulted in a heliocentric orbit with a perihelion of 0.99 AU and aphelion ~1.7 AU.

It is now catalogued as such.

You can find out where it is now and where it is going and how fast at https://www.whereisroadster.com/

So a "how fast could it go" question really depends on what orbit you put it in. If you aim for a highly elliptical heliocentric orbit then at perihelion (closest to the Sun) it will be going a lot faster than at aphelion one-half period later.

I think that ultimately you question could best be phrased as

What is the air speed velocity of an unladen swallow Falcon?

To which the answer is

African or European?

or even better:

What heliocentric $C_3$ can a Falcon 9 achieve with zero payload?

For more on $C_3$ see https://space.stackexchange.com/search?q=user%3A265+C3

Partial answer only.

This could turn out to be quite a complicated question to answer fully, but it turns out that they've done the experiment for the Falcon Heavy and we know the answer for that one at least.

The Tesla Roadster launched first to a high apoapsis (about 7000 km) elliptical LEO orbit and stayed there for 6 hours and then went off to deep space by burning every last bit of propellant.

That resulted in a heliocentric orbit with a perihelion of 0.99 AU and aphelion ~1.7 AU.

It is now catalogued there.

So a "how fast could it go" question really depends on what orbit you put it in. If you aim for a highly elliptical heliocentric orbit then at perihelion (closest to the Sun) it will be going a lot faster than at aphelion one-half period later.

I think that ultimately you question could best be phrased as

What is the air speed velocity of an unladed swallow Falcon?

To which the answer is

African or European?

or even better:

What heliocentric $C_3$ can a Falcon 9 achieve with zero payload?

For more on $C_3$ see https://space.stackexchange.com/search?q=user%3A265+C3

Partial answer only.

This could turn out to be quite a complicated question to answer fully, but it turns out that they've done the experiment for the Falcon Heavy and we know the answer for that one at least.

The Tesla Roadster launched first to a high apoapsis (about 7000 km) elliptical LEO orbit and stayed there for 6 hours and then went off to deep space by burning every last bit of propellant.

That resulted in a heliocentric orbit with a perihelion of 0.99 AU and aphelion ~1.7 AU.

It is now catalogued as such.

You can find out where it is now and where it is going and how fast at https://www.whereisroadster.com/

So a "how fast could it go" question really depends on what orbit you put it in. If you aim for a highly elliptical heliocentric orbit then at perihelion (closest to the Sun) it will be going a lot faster than at aphelion one-half period later.

I think that ultimately you question could best be phrased as

What is the air speed velocity of an unladed swallow Falcon?

To which the answer is

African or European?

or even better:

What heliocentric $C_3$ can a Falcon 9 achieve with zero payload?

For more on $C_3$ see https://space.stackexchange.com/search?q=user%3A265+C3