Short answer. Often yes, and to your benefit. Where the pleading states a common cause of action against several defendants and some answer while others do not, the court tries the case against all of them on the answers filed, and renders judgment on the evidence presented.
What the law says
When a pleading asserting a claim states a common cause of action against several defending parties, some of whom answer and the others fail to do so, the court shall try the case against all upon the answers thus filed and render judgment upon the evidence presented.
Rule 9, Section 3 — Default; [d]eclaration of. Read the full provision →
Partial default does not mean automatic loss
This is one of the few places in procedure where another party's diligence protects you. The ordinary consequence of not answering is a judgment resting on the pleading alone. But where the cause of action is common to several defendants and at least one of them answers, the rule directs the court to try the case against all upon the answers filed, and to render judgment upon the evidence presented. The answering defendant's defence is effectively tested for everyone, and the claimant has to prove the case at trial rather than simply collecting on your silence.
Everything turns on the cause of action being common
The protection is not general. It applies where the pleading states a common cause of action against the several defending parties, meaning the claim against each rests on the same facts and the same theory, so that a defence defeating it for one would defeat it for all. Where the claims are genuinely separate, or where your liability rests on facts peculiar to you, that reasoning does not carry across and your failure to answer is judged on its own. Read the complaint to work out which situation you are actually in before assuming you are covered.
You are still a party in default
Being carried along by a co-defendant's answer is not the same as being a participating party. You have filed no responsive pleading, so the consequences of default still attach to you: you are entitled to notice of subsequent proceedings, but you do not take part in the trial. You cannot run your own defence, call your own witnesses, or cross-examine. If the answering defendant settles, withdraws, or defends on a theory that suits their position and not yours, you have no ability to redirect any of it.
The safer course
If the deadline has passed but no judgment has yet been rendered, the rule still allows a motion under oath to set aside the order of default, on a showing that the failure to answer was due to fraud, accident, mistake or excusable negligence and that you have a meritorious defence. Treating partial default as a strategy is a poor trade, because it leaves your outcome in someone else's hands. Use the time before judgment to get back into the case properly.