In the US, at least, union wages would have brought in $20-30 or so per week. [1] Looking through [2], you could get a whole gentleman's outfit for roughly $50 or so. Even still, you'd be spending 2-3 weeks' wages on a single set of clothing - not to mention that you'd need somewhere to store all that, and you'd probably also need additional stuff to maintain it so that it looked half-presentable for your daring escape.
It's much more likely that, as someone in steerage, even your "finest" wouldn't have passed muster for the keenly class-conscious Brits on the upper decks. The fabrics and cuts would be different, you'd be missing fashionable accessories and key pieces of the outfit, nothing would be tailored, and everything would be in worse wear. (Not to mention your lower-class accent and diction would likely give you away, unless you'd somehow had the benefit of a pricey elocution tutor.)
[1] https://fraser.stlouisfed.org/title/union-scale-wages-hours-... [2] https://vintagedancer.com/1900s/edwardian-1910s-historical-m...