I would say no. Generosity is one of our ways of being Christ to one another. What I mean is that all generous acts are a form a God’s grace acting through us. However, God’s grace is not going to be acting through us if we are knowingly neglecting another area of our life that needs attention. It is here that the virtues of temperance and prudence come in.
If a person is ignoring another person’s (including his own) legitimate means because an excess of giving in one area of his life, then he ceases to be generous.