Yes it does, SnapBill currently supports billing in every currency. To enable or disable support for each currency you can go to Setup -> Billing -> Currencies.

Once you have enabled support for a chosen currency you will be able to create new accounts with the currency, and invoice clients accordingly.

Supported currencies:

United Arab Emirates Dirham	AED
Afghan Afghani	AFN
Albanian Lek	ALL
Armenian Dram	AMD
Netherlands Antillean Guilder	ANG
Angolan Kwanza	AOA
Argentine Peso	ARS
Australian Dollar	AUD
Aruban Florin	AWG
Azerbaijani Manat	AZN
Bosnia-Herzegovina Convertible Mark	BAM
Barbados Dollar	BBD
Bangladeshi Taka	BDT
Bulgarian Lev	BGN
Bahraini Dinar	BHD
Burundian Franc	BIF
Bermuda Dollar	BMD
Brunei Dollar	BND
Bolivian Boliviano	BOB
Brazilian Real	BRL
Bahamian Dollar	BSD
Bhutanese Ngultrum	BTN
Botswana Pula	BWP
Belarusian Ruble	BYR
Belize Dollar	BZD
Canadian Dollar	CAD
Franc Congolais	CDF
Swiss Franc	CHF
Chilean Peso	CLP
Chinese Yuan	CNY
Colombian Peso	COP
Costa Rican Colon	CRC
Cape Verde Escudo	CVE
Czech Koruna	CZK
Djiboutian Franc	DJF
Danish Krone	DKK
Dominican Peso	DOP
Algerian Dinar	DZD
Estonian Kroon	EEK
Egyptian Pound	EGP
Eritrean Nakfa	ERN
Ethiopian Birr	ETB
Euro	EUR
Fiji Dollar	FJD
Pound Sterling	GBP
Georgian Lari	GEL
Ghanaian Cedi	GHS
Gibraltar Pound	GIP
Gambian Dalasi	GMD
Guinean Franc	GNF
Guatemalan Quetzal	GTQ
Guyanese Dollar	GYD
Hong Kong Dollar	HKD
Honduran Lempira	HNL
Croatian Kuna	HRK
Haitian Gourde	HTG
Hungarian Forint	HUF
Indonesian Rupiah	IDR
Israeli New Shekel	ILS
Indian Rupee	INR
Iraqi Dinar	IQD
Iranian Rial	IRR
Icelandic Krona	ISK
Jamaican Dollar	JMD
Jordanian Dinar	JOD
Japanese Yen	JPY
Kenyan Shilling	KES
Kyrgyzstani Som	KGS
Cambodian Riel	KHR
Comorian Franc	KMF
North Korean Won	KPW
Korean Won	KRW
Kuwaiti Dinar	KWD
Cayman Islands Dollar	KYD
Kazakhstani Tenge	KZT
Lao Kip	LAK
Lebanese Pound	LBP
Sri Lankan Rupee	LKR
Liberian Dollar	LRD
Lesotho Loti	LSL
Lithuanian Litas	LTL
Latvian Lats	LVL
Libyan Dinar	LYD
Moroccan Dirham	MAD
Moldovan Leu	MDL
Malagasy Ariary	MGA
Macedonia Denar	MKD
Myanmar Kyat	MMK
Mongolian Tugrik	MNT
Macau Pataca	MOP
Mauritania Ouguiya	MRO
Mauritian Rupee	MUR
Maldives Rufiyaa	MVR
Malawian Kwacha	MWK
Mexican Peso	MXN
Malaysian Ringgit	MYR
New Mozambican Metical	MZN
Namibian Dollar	NAD
Nigerian Naira	NGN
Nicaraguan Cordoba Oro	NIO
Norwegian Krone	NOK
Nepalese Rupee	NPR
New Zealand Dollar	NZD
Omani Rial	OMR
Panamanian Balboa	PAB
Peruvian Nuevo Sol	PEN
Papua New Guinea Kina	PGK
Philippine Peso	PHP
Pakistan Rupee	PKR
Polish Zloty	PLN
Paraguay Guarani	PYG
Qatari Riyal	QAR
Romanian Leu	RON
Serbian Dinar	RSD
Russian Ruble	RUB
Rwandan Franc	RWF
Saudi Arabian Riyal	SAR
Solomon Islands Dollar	SBD
Seychelles Rupee	SCR
Sudanese Pound	SDG
Swedish Krona	SEK
Singapore Dollar	SGD
Saint Helena Pound	SHP
Sierra Leonean Leone	SLL
Somali Shilling	SOS
Suriname Dollar	SRD
Sao Tome Dobra	STD
Syrian Pound	SYP
Swazi Lilangeni	SZL
Thai Baht	THB
Tajikistan Somoni	TJS
Tunisian Dinar	TND
Tongan Pa'Anga	TOP
New Turkish Lira	TRY
Trinidad and Tobago Dollar	TTD
New Taiwan Dollar	TWD
Tanzanian Shilling	TZS
Ukrainian Hryvnia	UAH
Uganda Shilling	UGX
United States Dollar	USD
Uruguayan peso	UYU
Uzbekistani Som	UZS
Venezuelan Bolivar Fuerte	VEF
Viet Nam Dong	VND
Vanuatu Vatu	VUV
Samoa Tala	WST
Central African CFA	XAF
East Caribbean Dollar	XCD
West African CFA	XOF
French Pacific Franc	XPF
Yemeni Rial	YER
South African Rand	ZAR
Zambian Kwacha	ZMK