The lumped model of a wire (or any other element) is an approximation. It's not entirely accurate, but it can be useful in many circumstances.
The distributed transmission line model given by the telegrapher's equations is another approximation. It's useful in some circumstances where the lumped model becomes very inaccurate. But it will itself break down and be inaccurate in some cases.
If you are worried that the lumped approximation might not be accurate enough in your situation, you should solve your problem both ways (or maybe a small piece of your problem that will reveal the scale of the discrepancy between the models). If the difference is big enough to affect the final conclusions you are trying to draw from the model, then you should use the transmission line model. If the differences are too small to affect your conclusions, then you may be able to save some time and effort by using the lumped-element model.
Continuous varying impedances are used all the time for impedance matching. If you have a very capacitive part of a trace (for example, where a large component pad might be), you can have a relatively inductive transition before or after it to "balance" it out.
What will end up happening is that the reflections will "stack up" but, instead of being at one point (a VSWR peak), it will be moderately spread out. You can still imagine it discretely, but in small steps.
And also remember, if you have a small reflection point, any backward reflection after THAT will be reflected slightly FORWARD, and so on.
Anyway, the good gents at http://www.microwaves101.com/encyclopedia/klopfenstein.cfm always have a nice, in depth explanation.
edit: I didn't completely answer your question. "How it would look" is dependent a bit on how you are describing it. In the frequency domain, what you'll probably get is a VSWR that is "de-Q'd". You'll go from a nice sharp peak at midband to a more gradual, broader band response.
In the time domain....well, I don't work with the time domain as much but I would imagine you would have a lower amplitude, longer pulsewidth "ringing" or reflection.
Best Answer
The height of a line (thickness of dielectric) affects both its capacitance and inductance. The width of a line affects both its capacitance and inductance. The length of a line affects only its delay, and its attenuation.
If a transmitter and an antenna are the same impedance, and connected by a line of that impedance, then the length of the line connecting them is irrelevant (except for ohmic losses causing attenuation).
However, often the transmitter isn't matched for some reason, power or efficiency, and the antenna may not be matched, perhaps for space, and the line between them is used for matching. In that case, the maximum matching effect can be achieved with a \$\lambda/4\$ or odd multiples of that length line. With a \$\lambda/2\$ line or multiples, no matching impedance transformation is achieved, regardless of the line impedance.