The only danger is miscarriage, and since Alex doesn't want this baby, why the fuck should he care? He should tell her to get a test, and if she doesn't, she's on her own and he will refuse to recognize the child.
In fact, he should tell her she's on her own in any case, and he doesn't give a shit about her being pregnant. Since she's richer than him, she can't even ask for child supports. She may consider him an anonymous donor and if she tries to go public on this, she'll regret it.