Useless? No. Challenging? Yes.
A progressive tax system hinges on the ability of the state to levy and collect relatively higher taxes on relatively higher incomes and wealth.
The ability to levy is simple: write a law that mandates a higher rate or broader base for a higher band of income or wealth. Tax loopholes and offshore bank accounts do not hinder levying as such, although they may increase the relative financial power of certain groups of taxpayers, thereby strengthening their ability to lobby the legislature to impose less progressive taxation.
The ability to collect, however, may be substantially hindered by tax loopholes and offshore bank accounts. To be clear, there is nothing illegal or immoral by definition of benefiting from a tax loophole or an offshore bank account. Loopholes emerge all the time as a consequence of poorly assessed legislation or unintended consequences, while an offshore bank account may be used for a host of purposes unrelated to escaping taxation. However, from the context of the question, the assumption here is that we are talking about exactly that - the undue taking advantage of loopholes and offshore bank accounts for the purposes of avoiding or evading taxation.
The use of such mechanisms to escape taxation may reduce the progressiveness of the tax system due to the ability of certain taxpayers to escape tax collection. Since this 'ability to escape' rises with income and wealth - we know that wealthy taxpayers are more likely and able to engage in aggressive tax planning practices - progressiveness is weakened, leaving a relatively higher tax burden on those taxpayers not able to escape, i.e. the less-well-off.
The ability to escape is well-known and built into standard models of tax systems. You may have heard of the Laffer curve, which stipulates that at a certain point, increasing the tax rate will result in negative revenue. This is partly due to the escape factor - the incentive to escape increases with the tax rate, thus limiting the extra revenue that can be collected for higher levels of taxation. It is also, for instance, a prime argument for the continued lowering of corporate income tax rates around the world, which is said to combat widespread base erosion and profit shifting by multinationals. Indeed, the tax economics literature tells us that we can reduce multinational profit shifting substantially by lowering the corporate income tax rate.
However, as I have written elsewhere, this is now changing. The global crackdown on tax evasion, tax avoidance and tax havens through expanded tax transparency and global tax information exchange may very well have strengthened states' ability to collect progressive taxation. The ability to escape has weakened. This allows states to levy more progressive taxes and increases the economically optimal levels of taxation, shifting some of the tax burden back on to mobile taxpayers.
Thus, while tax loopholes and offshore bank accounts may provide a substantial challenge to progressive taxation, they do not render progressiveness useless or impossible, and in fact international tax cooperation is improving the ability of countries to levy progressive taxation.