We investigate the viability of observing charged Higgs bosons (H^±H^\pm) produced in association with WW bosons at the CERN large hadron collider, using the leptonic decay H⁺ ®t⁺ n_tH^+ \to\tau^+ \nu_\tau and hadronic WW decay, within different scenarios of the minimal supersymmetric standard model (MSSM) with both real and complex parameters. Performing a parton level study we show how the irreducible standard model background from W+2W+2 jets can be controlled by applying appropriate cuts and find that the size of a possible signal depends on the cuts needed to suppress QCD backgrounds and misidentifications. In the standard maximal mixing scenario of the MSSM we find a viable signal for large tanb\tan\beta and intermediate H^±H^\pm masses ( ~ m_t{\sim} m_t) when using softer cuts ( p_^\textmissp_{\perp\text{miss}}, $p_{\perp\tau{\text{jet}}} >$p_{\perp\tau{\text{jet}}} > 50 GeV), whereas for harder cuts ( p_^\textmissp_{\perp\text{miss}}, $p_{\perp\tau{\text{jet}}} >$p_{\perp\tau{\text{jet}}} > 100 GeV) we only find a viable signal for very large tanb\tan\beta (>~50\gtrsim50). We have also investigated a special class of MSSM scenarios with large mass splittings among the heavy Higgs bosons where the cross-section can be resonantly enhanced by factors up to one hundred, with a strong dependence on the CPCP-violating phases. Even so we find that the signal after cuts remains small except for small masses (<~ m_t{\lesssim} m_t) when using the softer cuts. Finally, in all the scenarios we have investigated we have only found small CPCP-asymmetries.