Does the delocalization of p-orbitals ensure conductivity?
Delocalized $\pi$ orbitals do allow for mobile charges. The catch there is "allow." Just because these systems can have mobile charges does not make them conductive.

Conductivity can be defined as:
$\sigma = n e \mu$
where $e$ is the charge on an electron, $\mu$ is the charge mobility, and $n$ is the number of charges.

In the case of $doped$ conjugated polymers like you indicate above, the halogen vapors or other dopants usually oxidize the polymer and create more charges (i.e., $n$) and the conductivity increases. This does happen with pretty much every conjugated system I've seen: oxidize or reduce the neutral system and you'll have more charge carriers = greater conductivity. (NB: most conjugated organics are easier to oxidize than reduce, so you get + charges (holes) as the charge carrier, rather than electrons.)

That's the quick explanation as to why adding halogens increases the conductivity -- you get more charge carriers.

Incidentally, there are other ways to increase the charge carriers. Chemical or electrochemical doping usually makes a conductive system, but you can also use electrical bias (e.g., a field-effect transistor) or light (i.e., a photovoltaic) which will also increase carrier concentrations.

As to why trans-polyacetylene isn't a metal in the first place?

If we use a simple particle-in-a-box model, the difference in energy levels goes to zero as the box becomes very large. This would suggest trans-polyacetylene should be a metal (i.e., no band gap).

Consider also the Hückel model for polyacetylene. We can build up the nearly-infinite system by solving for ethylene, butadiene, etc.



Notice that the energy gap between levels becomes smaller and smaller. We can plot the HOMO-LUMO gap as a function of chain length:



The gap becomes smaller and smaller! 

Wikipedia even gives the general formulas:

$$E_k = \alpha + 2\beta \cos \frac{k\pi}{(n+1)}$$
$$\Delta E = -4\beta \sin \frac{\pi}{2(n+1)}$$

So both particle in a box and Hückel predict no band gap when $n$ gets very large. Theory predicts a metal!

Why doesn't the real polyacetylene behave as a metal. For any one-dimensional system, there will be a Peierls distortion which lowers the total energy by distorting the geometry (long-short bond alternation) and increasing the band gap.1

In short, a truly one-dimensional metal is impossible, but doped polymers are certainly very good electrical conductors. Record films of trans-polyacetlyene have conductivity close to conventional metals.2






1 The long-short bond alternation is the Peierls distortion. It means some electrons are localized (shorter double bonds) and thus lower in energy. This creates a band gap (i.e., lower E for valence band).

2 The film isn't a 1D material, but the trans-polyacetylene chains are each 1D.