We have many posts here discussing restriction practice, including various strategies for when and when not to traverse and/or petition restrictions.
One issue that arises in the context of restriction is rejoinder. As discussed in MPEP 821.04, rejoinder involves withdrawal of a restriction between an allowed elected claim and a non-elected invention (which depends from or otherwise requires all limitations of an allowable claim, for example). Relevant portions of MPEP 821.04 are reproduced below:
821.04 Rejoinder [R-08.2012]
The propriety of a restriction requirement should be reconsidered when all the claims directed to the elected invention are in condition for allowance, and the nonelected invention(s) should be considered for rejoinder. Rejoinder involves withdrawal of a restriction requirement between an allowable elected invention and a nonelected invention and examination of the formerly nonelected invention on the merits.
In order to be eligible for rejoinder, a claim to a nonelected invention must depend from or otherwise require all the limitations of an allowable claim. A withdrawn claim that does not require all the limitations of an allowable claim will not be rejoined. Furthermore, where restriction was required between a product and a process of making and/or using the product, and the product invention was elected and subsequently found allowable, all claims to a nonelected process invention must depend from or otherwise require all the limitations of an allowable claim for the claims directed to that process invention to be eligible for rejoinder. See MPEP § 821.04(b). In order to retain the right to rejoinder, applicant is advised that the claims to the nonelected invention(s) should be amended during prosecution to require the limitations of the elected invention. Failure to do so may result in a loss of the right to rejoinder.
Rejoined claims must be fully examined for patentability in accordance with 37 CFR 1.104. Thus, to be allowable, the rejoined claims must meet all criteria for patentability including the requirements of 35 U.S.C. 101, 102, 103 and 112.
Now, rejoinder is not dependent on the applicant traversing the restriction. But, the procedure that the Examiner follows can often mean that unless the applicant traverses, the applicant does not get a reasonable chance to amend claims to make them eligible for rejoinder. This is in part because of MPEP 821.02 Form Paragraph 8.07 “Ready for Allowance, Non-elected Claims Withdrawn Without Traverse.” What happens here is that the Examiner decides whether to rejoin and if not, cancels the claims and issues a notice of allowance. While the applicant has to agree to cancel the claims, the applicant may not get a real chance to amend non-elected claims to make them eligible for rejoinder.
If the applicant traversed, then Form Paragraph 8.03 is used and the Applicant has the chance to see if something can be done to rejoin more claims.
8.03 In Condition for Allowance, Non-elected Claims Withdrawn with Traverse
This application is in condition for allowance except for the presence of claim  directed to an invention non-elected with traverse in the reply filed on . Applicant is given TWO MONTHS from the date of this letter to cancel the noted claims or take other appropriate action (37 CFR 1.144). Failure to take action during this period will be treated as authorization to cancel the noted claims by Examiner’s Amendment and pass the case to issue. Extensions of time under 37 CFR 1.136(a) will not be permitted since this application will be passed to issue.
The prosecution of this case is closed except for consideration of the above matter.
See also MPEP § 821.04 for rejoinder of certain nonelected inventions when the claims to the elected invention are allowable.
When preparing a final action in an application where there has been a traversal of a requirement for restriction, the examiner should indicate in the Office action which claims, if any, remain withdrawn from consideration.
Note that the petition under 37 CFR 1.144 must be filed not later than appeal. This is construed to mean on or before the date the notice of appeal is filed. See MPEP § 1204. If the application is ready for allowance on or after the date of the notice of appeal and no petition has been filed, the examiner should simply cancel nonelected claims that are not eligible for rejoinder by examiner’s amendment, calling attention to the provisions of 37 CFR 1.144.
For applicants that cannot afford multiple divisional applications, every little bit that can be done to maximize coverage in the original application helps.
So yes, you can rejoin even without traverse. But, a traverse gives the applicant the option to review and confirm that they agree with the Examiner’s decision on rejoinder or the lack thereof, and possibly find a way to make some adjustments and have more claims rejoined. Just another benefit of a traverse.